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Factoring determinants and applications to number theory Random Matrices Theory Appl. (IF 0.9) Pub Date : 20240527
Estelle Basor, Brian ConreyProducts of shifted characteristic polynomials, and ratios of such products, averaged over the classical compact groups are of great interest to number theorists as they model similar averages of Lfunctions in families with the same symmetry type as the compact group. We use Toeplitz and Toeplitz plus Hankel operators and the identities of Borodin–Okounkov–Case–Geronimo, and Basor–Ehrhardt to prove

Dynamics of a rankone multiplicative perturbation of a unitary matrix Random Matrices Theory Appl. (IF 0.9) Pub Date : 20240521
Guillaume Dubach, Jana RekerWe provide a dynamical study of a model of multiplicative perturbation of a unitary matrix introduced by Fyodorov. In particular, we identify a flow of deterministic domains that bound the spectrum with high probability, separating the outlier from the typical eigenvalues at all subcritical timescales. These results are obtained under generic assumptions on U that hold for a variety of unitary random

Monotonicity of the logarithmic energy for random matrices Random Matrices Theory Appl. (IF 0.9) Pub Date : 20240521
Djalil Chafaï, Benjamin Dadoun, Pierre YoussefIt is well known that the semicircle law, which is the limiting distribution in the Wigner theorem, is the minimizer of the logarithmic energy penalized by the second moment. A very similar fact holds for the Girko and Marchenko–Pastur theorems. In this work, we shed the light on an intriguing phenomenon suggesting that this functional is monotonic along the mean empirical spectral distribution in

Eigenvalue distributions of highdimensional matrix processes driven by fractional Brownian motion Random Matrices Theory Appl. (IF 0.9) Pub Date : 20240520
Jian Song, Jianfeng Yao, Wangjun YuanIn this paper, we study highdimensional behavior of empirical spectral distributions {LN(t),t∈[0,T]} for a class of N×N symmetric/Hermitian random matrices, whose entries are generated from the solution of stochastic differential equation driven by fractional Brownian motion with Hurst parameter H∈(1/2,1). For Wignertype matrices, we obtain almost sure relative compactness of {LN(t),t∈[0,T]}N∈ℕ in

Characteristic polynomials of orthogonal and symplectic random matrices, Jacobi ensembles & Lfunctions Random Matrices Theory Appl. (IF 0.9) Pub Date : 20240510
Mustafa Alper GunesStarting from Montgomery’s conjecture, there has been a substantial interest on the connections of random matrix theory and the theory of Lfunctions. In particular, moments of characteristic polynomials of random matrices have been considered in various works to estimate the asymptotics of moments of Lfunction families. In this paper, we first consider joint moments of the characteristic polynomial

Finite size corrections for real eigenvalues of the elliptic Ginibre matrices Random Matrices Theory Appl. (IF 0.9) Pub Date : 20240220
SungSoo Byun, YongWoo LeeIn this paper, we consider the elliptic Ginibre matrices in the orthogonal symmetry class that interpolates between the real Ginibre ensemble and the Gaussian orthogonal ensemble. We obtain the finite size corrections of the real eigenvalue densities in both the global and edge scaling regimes, as well as in both the strong and weak nonHermiticity regimes. Our results extend and provide the rate of

Asymptotic cyclicconditional freeness of random matrices Random Matrices Theory Appl. (IF 0.9) Pub Date : 20240131
Guillaume Cébron, Nicolas GilliersVoiculescu’s freeness emerges when computing the asymptotic spectra of polynomials on N×N random matrices with eigenspaces in generic positions: they are randomly rotated with a uniform unitary random matrix UN. In this paper, we elaborate on the previous result by proposing a random matrix model, which we name the Vortex model, where UN has the law of a uniform unitary random matrix conditioned to

The distribution of sample meanvariance portfolio weights Random Matrices Theory Appl. (IF 0.9) Pub Date : 20240131
Raymond Kan, Nathan Lassance, Xiaolu WangWe present a simple stochastic representation for the joint distribution of sample estimates of three scalar parameters and two vectors of portfolio weights that characterize the minimumvariance frontier. This stochastic representation is useful for sampling observations efficiently, deriving moments in closedform, and studying the distribution and performance of many portfolio strategies that are

Asymptotics of the determinant of the modified Bessel functions and the second Painlevé equation Random Matrices Theory Appl. (IF 0.9) Pub Date : 20240131
Yu Chen, ShuaiXia Xu, YuQiu ZhaoIn the paper, we consider the extended Gross–Witten–Wadia unitary matrix model by introducing a logarithmic term in the potential. The partition function of the model can be expressed equivalently in terms of the Toeplitz determinant with the (i,j)entry being the modified Bessel functions of order i−j−ν, ν∈ℂ. When the degree n is finite, we show that the Toeplitz determinant is described by the isomonodromy

The Boolean quadratic forms and tangent law Random Matrices Theory Appl. (IF 0.9) Pub Date : 20240129
Wiktor Ejsmont, Patrycja HęćkaIn [W. Ejsmont and F. Lehner, The free tangent law, Adv. Appl. Math. 121 (2020) 102093], we study the limit sums of free commutators and anticommutators and show that the generalized tangent function tanz1−xtanz describes the limit distribution. This is the generating function of the higher order tangent numbers of Carlitz and Scoville (see (1.6) in [L. Carlitz and R. Scoville, Tangent numbers and

On special solutions to the Ermakov–Painlevé XXV equation Random Matrices Theory Appl. (IF 0.9) Pub Date : 20240103
Alexander Chichurin, Galina FilipukIn this paper, we study a nonlinear secondorder ordinary differential equation which we call the Ermakov–Painlevé XXV equation since under certain restrictions on its coefficients it can be reduced either to the Ermakov or the Painlevé XXV equation. The Ermakov–Painlevé XXV equation arises from a generalized Riccati equation and the related thirdorder linear differential equation via the Schwarzian

Tail bounds on the spectral norm of subexponential random matrices Random Matrices Theory Appl. (IF 0.9) Pub Date : 20231124
Guozheng Dai, Zhonggen Su, Hanchao WangLet X be an n×n symmetric random matrix with independent but nonidentically distributed entries. The deviation inequalities of the spectral norm of X with Gaussian entries have been obtained by using the standard concentration of Gaussian measure results. This paper establishes an upper tail bound of the spectral norm of X with subexponential entries. Our method relies upon a crucial ingredient of

Rank 1 perturbations in random matrix theory — A review of exact results Random Matrices Theory Appl. (IF 0.9) Pub Date : 20230819
Peter J. ForresterA number of random matrix ensembles permitting exact determination of their eigenvalue and eigenvector statistics maintain this property under a rank 1 perturbation. Considered in this review are the additive rank 1 perturbation of the Hermitian Gaussian ensembles, the multiplicative rank 1 perturbation of the Wishart ensembles, and rank 1 perturbations of Hermitian and unitary matrices giving rise

Limiting spectral distribution of stochastic block model Random Matrices Theory Appl. (IF 0.9) Pub Date : 20230718
Giap Van Su, MayRu Chen, MeiHui Guo, HaoWei HuangThe stochastic block model (SBM) is an extension of the Erdős–Rényi graph and has applications in numerous fields, such as data analysis, recovering community structure in graph data and social networks. In this paper, we consider the normal central SBM adjacency matrix with K communities of arbitrary sizes. We derive an explicit formula for the limiting empirical spectral density function when the

Matrix deviation inequality for ℓpnorm Random Matrices Theory Appl. (IF 0.9) Pub Date : 20230615
YuanChung Sheu, TeChun WangMotivated by the general matrix deviation inequality for i.i.d. ensemble Gaussian matrix [R. Vershynin, HighDimensional Probability: An Introduction with Applications in Data Science, Cambridge Series in Statistical and Probabilistic Mathematics (Cambridge University Press, 2018), doi:10.1017/9781108231596 of Theorem 11.1.5], we show that this property holds for the ℓpnorm with 1≤p<∞ and i.i.d. ensemble

Central limit theorem for linear spectral statistics of blockWignertype matrices Random Matrices Theory Appl. (IF 0.9) Pub Date : 20230607
Zhenggang Wang, Jianfeng YaoMotivated by the stochastic block model, we investigate a class of Wignertype matrices with certain block structures and establish a CLT for the corresponding linear spectral statistics (LSS) via the largedeviation bounds from local law and the cumulant expansion formula. We apply the results to the stochastic block model. Specifically, a class of renormalized adjacency matrices will be blockWignertype

Limit theorems for moment processes of beta Dyson’s Brownian motions and beta Laguerre processes Random Matrices Theory Appl. (IF 0.9) Pub Date : 20230314
Fumihiko Nakano, Hoang Dung Trinh, Khanh Duy TrinhIn the regime where the parameter beta is proportional to the reciprocal of the system size, it is known that the empirical distribution of Gaussian beta ensembles (respectively, beta Laguerre ensembles) converges weakly to a probability measure of associated Hermite polynomials (respectively, associated Laguerre polynomials), almost surely. Gaussian fluctuations around the limit have been known as

Global eigenvalue fluctuations of random biregular bipartite graphs Random Matrices Theory Appl. (IF 0.9) Pub Date : 20230218
Ioana Dumitriu, Yizhe ZhuWe compute the eigenvalue fluctuations of uniformly distributed random biregular bipartite graphs with fixed and growing degrees for a large class of analytic functions. As a key step in the proof, we obtain a total variation distance bound for the Poisson approximation of the number of cycles and cyclically nonbacktracking walks in random biregular bipartite graphs, which might be of independent

The moderate deviation principles of likelihood ratio tests under alternative hypothesis Random Matrices Theory Appl. (IF 0.9) Pub Date : 20230109
Yansong Bai, Yong ZhangLet x1,…,xn be independent and identically distributed (i.i.d.) realvalued random vectors from distribution Np(μ,Σ), where the sample size n and the vector dimension p satisfy n−1>p→∞. We are interested in the exponential convergence rate of the likelihood ratio test (LRT) statistics for testing Σ equal to a given matrix and (μ,Σ) equal to a given pair. In traditional statistical theory, the LRT statistics

Random matrix theory and moments of moments of Lfunctions Random Matrices Theory Appl. (IF 0.9) Pub Date : 20221208
J. C. Andrade, C. G. BestIn this paper, we give an analytic proof of the asymptotic behavior of the moments of moments of the characteristic polynomials of random symplectic and orthogonal matrices. We therefore obtain alternate, integral expressions for the leading order coefficients previously found by Assiotis, Bailey and Keating. We also discuss the conjectures of Bailey and Keating for the corresponding moments of moments

Asymptotic properties of GEE with diverging dimension of covariates Random Matrices Theory Appl. (IF 0.9) Pub Date : 20221112
Chunhua Zhu, Qibing Gao, Yi YaoIn this paper, for the generalized estimating equation (GEE) with diverging number of covariates, the asymptotic properties of GEE estimator are considered. Under the weaker assumption on the minimum eigenvalue of Fisher information matrix and some other regular conditions, we prove the asymptotic existence, consistency and asymptotic normality of the GEE estimator and the asymptotic distribution of

Quantum interpolating ensemble: Biorthogonal polynomials and average entropies Random Matrices Theory Appl. (IF 0.9) Pub Date : 20221026
Lu Wei, Nicholas WitteThe density matrix formalism is a fundamental tool in studying various problems in quantum information processing. In the space of density matrices, the most wellknown measures are the Hilbert–Schmidt and Bures–Hall ensembles. In this work, the averages of quantum purity and von Neumann entropy for an ensemble that interpolates between these two major ensembles are explicitly calculated for finitedimensional

Nonlinear interaction detection through partial dimension reduction with missing response data Random Matrices Theory Appl. (IF 0.9) Pub Date : 20221013
HongXia Xu, GuoLiang Fan, JinChang LiIn this paper, we are concerned with nonlinear interaction detection based on partial dimension reduction with missing response data. The covariates are grouped through linear combinations in a general class of semiparametric models to detect their joint interaction effects. The joint interaction effects are estimated by a profile least squares approach with the help of the inverse probability weighted

Covariance kernel of linear spectral statistics for halfheavy tailed Wigner matrices Random Matrices Theory Appl. (IF 0.9) Pub Date : 20220912
Asad Lodhia, Anna MaltsevIn this paper, we analyze the covariance kernel of the Gaussian process that arises as the limit of fluctuations of linear spectral statistics for Wigner matrices with a few moments. More precisely, the process we study here corresponds to Hermitian matrices with independent entries that have α moments for 2<α<4. We obtain a closed form αdependent expression for the covariance of the limiting process

Spectral measure of empirical autocovariance matrices of highdimensional Gaussian stationary processes Random Matrices Theory Appl. (IF 0.9) Pub Date : 20220822
Arup Bose, Walid HachemConsider the empirical autocovariance matrices at given nonzero time lags, based on observations from a multivariate complex Gaussian stationary time series. The spectral analysis of these autocovariance matrices can be useful in certain statistical problems, such as those related to testing for white noise. We study the behavior of their spectral measure in the asymptotic regime where the time series

Asymptotic freeness of unitary matrices in tensor product spaces for invariant states Random Matrices Theory Appl. (IF 0.9) Pub Date : 20220810
Benoît Collins, Pierre Yves Gaudreau Lamarre, Camille MaleIn this paper, we pursue our study of asymptotic properties of families of random matrices that have a tensor structure. In [6], the first and second authors provided conditions under which tensor products of unitary random matrices are asymptotically free with respect to the normalized trace. Here, we extend this result by proving that asymptotic freeness of tensor products of Haar unitary matrices

Characteristic polynomials of random truncations: Moments, duality and asymptotics Random Matrices Theory Appl. (IF 0.9) Pub Date : 20220728
Alexander Serebryakov, Nick Simm, Guillaume DubachWe study moments of characteristic polynomials of truncated Haar distributed matrices from the three classical compact groups O(N), U(N) and Sp(2N). For finite matrix size we calculate the moments in terms of hypergeometric functions of matrix argument and give explicit integral representations highlighting the duality between the moment and the matrix size as well as the duality between the orthogonal

Limiting eigenvalue behavior of a class of large dimensional random matrices formed from a Hadamard product Random Matrices Theory Appl. (IF 0.9) Pub Date : 20220728
Jack W. SilversteinThis paper investigates the strong limiting behavior of the eigenvalues of the class of matrices 1N(Dn∘Xn)(Dn∘Xn)∗, studied in [V. L. Girko, Theory of Stochastic Canonical Equations: Vol. 1 (Kluwer Academic Publishers, Dordrecht, 2001)]. Here, Xn=(xij) is an n×N random matrix consisting of independent complex standardized random variables, Dn=(dij), n×N, has nonnegative entries, and ∘ denotes Hadamard

On the analytic structure of secondorder noncommutative probability spaces and functions of bounded Fréchet variation Random Matrices Theory Appl. (IF 0.9) Pub Date : 20220722
Mario Diaz, James A. MingoIn this paper, we propose a new approach to the central limit theorem (CLT) based on functions of bounded Fréchet variation for the continuously differentiable linear statistics of random matrix ensembles which relies on a weaker form of a large deviation principle for the operator norm; a Poincarétype inequality for the linear statistics; and the existence of a secondorder limit distribution. This

Universal scaling limits of the symplectic elliptic Ginibre ensemble Random Matrices Theory Appl. (IF 0.9) Pub Date : 20220722
SungSoo Byun, Markus EbkeWe consider the eigenvalues of symplectic elliptic Ginibre matrices which are known to form a Pfaffian point process whose correlation kernel can be expressed in terms of the skeworthogonal Hermite polynomials. We derive the scaling limits and the convergence rates of the correlation functions at the real bulk/edge of the spectrum, which in particular establishes the local universality at strong nonHermiticity

Threedimensional Gaussian fluctuations of spectra of overlapping stochastic Wishart matrices Random Matrices Theory Appl. (IF 0.9) Pub Date : 20220722
Jeffrey Kuan, Zhengye ZhouIn [I. Dumitriu and E. Paquette, Spectra of overlapping Wishart matrices and the gaussian free field, Random Matrices: Theory Appl. 07(2) (2018) 1850003], the authors consider eigenvalues of overlapping Wishart matrices and prove that its fluctuations asymptotically convergence to the Gaussian free field. In this brief note, their result is extended to show that when the matrix entries undergo stochastic

Necessary and sufficient conditions for convergence to the semicircle distribution Random Matrices Theory Appl. (IF 0.9) Pub Date : 20220714
Calvin Wooyoung ChinWe consider random Hermitian matrices with independent upper triangular entries. Wigner’s semicircle law says that under certain additional assumptions, the empirical spectral distribution converges to the semicircle distribution. We characterize convergence to semicircle in terms of the variances of the entries, under natural assumptions such as the Lindeberg condition. The result extends to certain

On random matrices arising in deep neural networks: General I.I.D. case Random Matrices Theory Appl. (IF 0.9) Pub Date : 20220714
Leonid Pastur, Victor SlavinWe study the eigenvalue distribution of random matrices pertinent to the analysis of deep neural networks. The matrices resemble the product of the sample covariance matrices, however, an important difference is that the analog of the population covariance matrix is now a function of random data matrices (synaptic weight matrices in the deep neural network terminology). The problem has been treated

Operator level limit of the circular Jacobi βensemble Random Matrices Theory Appl. (IF 0.9) Pub Date : 20220712
Yun Li, Benedek ValkóWe prove an operator level limit for the circular Jacobi βensemble. As a result, we characterize the counting function of the limit point process via coupled systems of stochastic differential equations. We also show that the normalized characteristic polynomials converge to a random analytic function, which we characterize via the joint distribution of its Taylor coefficients at zero and as the solution

Some characterization results on classical and free Poisson thinning Random Matrices Theory Appl. (IF 0.9) Pub Date : 20220629
Soumendu Sundar MukherjeePoisson thinning is an elementary result in probability, which is of great importance in the theory of Poisson point processes. In this paper, we record a couple of characterization results on Poisson thinning. We also consider several free probability analogues of Poisson thinning, which we collectively dub as free Poisson, and prove characterization results for them, similar to the classical case

The partition function of loggases with multiple odd charges Random Matrices Theory Appl. (IF 0.9) Pub Date : 20220518
Elisha D. Wolff, Jonathan M. WellsWe use techniques in the shuffle algebra to present a formula for the partition function of a onedimensional loggas comprised of particles of (possibly) different integer charges at certain inverse temperature β in terms of the Berezin integral of an associated nonhomogeneous alternating tensor. This generalizes previously known results by removing the restriction on the number of species of odd

Edge fluctuations for random normal matrix ensembles Random Matrices Theory Appl. (IF 0.9) Pub Date : 20220516
David GarcíaZeladaA famous result going back to Eric Kostlan states that the moduli of the eigenvalues of random normal matrices with radial potential are independent yet nonidentically distributed. This phenomenon is at the heart of the asymptotic analysis of the edge, and leads in particular to the Gumbel fluctuation of the spectral radius when the potential is quadratic. In the present work, we show that a wide

Large deviations for spectral measures of some spiked matrices Random Matrices Theory Appl. (IF 0.9) Pub Date : 20220504
Nathan Noiry, Alain RouaultWe prove large deviations principles for spectral measures of perturbed (or spiked) matrix models in the direction of an eigenvector of the perturbation. In each model under study, we provide two approaches, one of which relying on large deviations principle of unperturbed models derived in the previous work “Sum rules via large deviations” (Gamboa et al. [Sum rules via large deviations, J. Funct.

Relating random matrix map enumeration to a universal symbol calculus for recurrence operators in terms of Bessel–Appell polynomials Random Matrices Theory Appl. (IF 0.9) Pub Date : 20220429
Nicholas M. Ercolani, Patrick WatersMaps are polygonal cellular networks on Riemann surfaces. This paper analyzes the construction of closed form general representations for the enumerative generating functions associated to maps of fixed but arbitrary genus. The method of construction developed here involves a novel asymptotic symbol calculus for difference operators based on the relation between spectral asymptotics for Hermitian random

Weak convergence of a collection of random functions defined by the eigenvectors of large dimensional random matrices Random Matrices Theory Appl. (IF 0.9) Pub Date : 20220423
Jack W. SilversteinFor each n, let Un be Haar distributed on the group of n×n unitary matrices. Let xn,1,…,xn,m denote orthogonal nonrandom unit vectors in ℂn and let un,k=(uk1,…,ukn)∗=Un∗xn,k, k=1,…,m. Define the following functions on [0,1]: Xnk,k(t)=n∑i=1[nt](uki2−1n), Xnk,k′(t)=2n∑i=1[nt]ūkiuk′i, k0 as n→∞. This result extends the result in [J. W. Silverstein, Ann. Probab. 18 (1990) 1174–1194]. These results are

Adaptive singular value shrinkage estimate for low rank tensor denoising Random Matrices Theory Appl. (IF 0.9) Pub Date : 20220419
Zerui Tao, Zhouping LiRecently, tensors are widely used to represent higherorder data with internal spatial or temporal relations, e.g. images, videos, hyperspectral images (HSIs). While the true signals are usually corrupted by noises, it is of interest to study tensor recovery problems. To this end, many models have been established based on tensor decompositions. Traditional tensor decomposition models, such as the

Adaptive singular value shrinkage estimate for low rank tensor denoising Random Matrices Theory Appl. (IF 0.9) Pub Date : 20220419
Zerui Tao, Zhouping LiRecently, tensors are widely used to represent higherorder data with internal spatial or temporal relations, e.g. images, videos, hyperspectral images (HSIs). While the true signals are usually corrupted by noises, it is of interest to study tensor recovery problems. To this end, many models have been established based on tensor decompositions. Traditional tensor decomposition models, such as the

A new decomposition for multivalued 3 × 3 matrices Random Matrices Theory Appl. (IF 0.9) Pub Date : 20220412
Aymen Ammar, Aref Jeribi, Bilel SaadaouiIn this paper, a new concept for a 3 × 3 block relation matrix is studied in a Banach space. It is shown that, under certain condition, we can investigate the Frobenius–Schur decomposition of relation matrices. Furthermore, we present some conditions which should allow the multivalued 3 × 3 matrices linear operator to be closable.

High–low temperature dualities for the classical βensembles Random Matrices Theory Appl. (IF 0.9) Pub Date : 20220405
Peter J. ForresterThe loop equations for the βensembles are conventionally solved in terms of a 1/N expansion. We observe that it is also possible to fix N and expand in inverse powers of β. At leading order, for the onepoint function W1(x) corresponding to the average of the linear statistic A=∑j=1N1/(x−λj) and after specialising to the classical weights, this reclaims well known results of Stieltjes relating the

High–low temperature dualities for the classical βensembles Random Matrices Theory Appl. (IF 0.9) Pub Date : 20220405
Peter J. ForresterThe loop equations for the βensembles are conventionally solved in terms of a 1/N expansion. We observe that it is also possible to fix N and expand in inverse powers of β. At leading order, for the onepoint function W1(x) corresponding to the average of the linear statistic A=∑j=1N1/(x−λj) and after specialising to the classical weights, this reclaims well known results of Stieltjes relating the

On the operator norm of a Hermitian random matrix with correlated entries Random Matrices Theory Appl. (IF 0.9) Pub Date : 20220319
Jana RekerWe consider a correlated N×N Hermitian random matrix with a polynomially decaying metric correlation structure. By calculating the trace of the moments of the matrix and using the summable decay of the cumulants, we show that its operator norm is stochastically dominated by one.

Generalized heterogeneous hypergeometric functions and the distribution of the largest eigenvalue of an elliptical Wishart matrix Random Matrices Theory Appl. (IF 0.9) Pub Date : 20220317
Aya Shinozaki, Koki Shimizu, Hiroki HashiguchiIn this paper, we derive the exact distributions of eigenvalues of a singular Wishart matrix under the elliptical model. We define the generalized heterogeneous hypergeometric functions with two matrix arguments and provide the convergence conditions of these functions. The joint density of eigenvalues and the distribution function of the largest eigenvalue for a singular elliptical Wishart matrix

Random matrices with independent entries: Beyond noncrossing partitions Random Matrices Theory Appl. (IF 0.9) Pub Date : 20220308
Arup Bose, Koushik Saha, Arusharka Sen, Priyanka SenThe scaled standard Wigner matrix (symmetric with mean zero, variance one i.i.d. entries), and its limiting eigenvalue distribution, namely the semicircular distribution, have attracted much attention. The 2kth moment of the limit equals the number of noncrossing pairpartitions of the set {1, 2,…, 2k}. There are several extensions of this result in the literature. In this paper, we consider a unifying

Joint CLT for top eigenvalues of sample covariance matrices of separable high dimensional long memory processes Random Matrices Theory Appl. (IF 0.9) Pub Date : 20220308
Peng TianFor N,n ∈ ℕ, consider the sample covariance matrix SN(T) = 1 NXX∗ from a data set X = CN1/2ZT n1/2, where Z = (Zi,j) is a N × n matrix having i.i.d. entries with mean zero and variance one, and CN,Tn are deterministic positive semidefinite Hermitian matrices of dimension N and n, respectively. We assume that (CN)N is bounded in spectral norm, and Tn is a Toeplitz matrix with its largest eigenvalues

Some strong convergence theorems for eigenvalues of general sample covariance matrices Random Matrices Theory Appl. (IF 0.9) Pub Date : 20211127
Yanqing YinThe aim of this paper is to investigate the spectral properties of sample covariance matrices under a more general population. We consider a class of matrices of the form Sn = 1 nBnXnXn∗B n∗, where Bn is a p × m nonrandom matrix and Xn is an m × n matrix consisting of i.i.d standard complex entries. p/n → c ∈ (0,∞) as n →∞ while m can be arbitrary but no smaller than p. We first prove that under some

A dynamical version of the SYK model and the qBrownian motion Random Matrices Theory Appl. (IF 0.9) Pub Date : 20211122
Miguel Pluma, Roland SpeicherWe extend recent results on the asymptotic eigenvalue distribution of the SYK model to the multivariate case and relate the limit of a dynamical version of the SYK model with the qBrownian motion, a noncommutative deformation of classical Brownian motion. Furthermore, we extend the results for fluctuations to the multivariate setting and treat also higher correlation functions. The structure of our

A dynamical version of the SYK model and the qBrownian motion Random Matrices Theory Appl. (IF 0.9) Pub Date : 20211122
Miguel Pluma, Roland SpeicherWe extend recent results on the asymptotic eigenvalue distribution of the SYK model to the multivariate case and relate the limit of a dynamical version of the SYK model with the qBrownian motion, a noncommutative deformation of classical Brownian motion. Furthermore, we extend the results for fluctuations to the multivariate setting and treat also higher correlation functions. The structure of our

On the empirical spectral distribution for certain models related to sample covariance matrices with different correlations Random Matrices Theory Appl. (IF 0.9) Pub Date : 20211117
Alicja DembczakKołodziejczyk, Anna LytovaGiven n,m ∈ ℕ, we study two classes of large random matrices of the form ℒn =∑α=1mξ αyαyαTand𝒜 n =∑α=1mξ α(yαxαT + x αyαT), where for every n, (ξα)α are iid copies of a random variable ξ = ξ(n) ∈ ℝ, (xα)α, (yα)α ⊂ ℝn are two (not necessarily independent) sets of independent random vectors having different covariance matrices and generating well concentrated bilinear forms. We consider two main asymptotic

On the asymptotic behavior of the eigenvalue distribution of block correlation matrices of highdimensional time series Random Matrices Theory Appl. (IF 0.9) Pub Date : 20211022
Philippe Loubaton, Xavier MestreWe consider linear spectral statistics built from the blocknormalized correlation matrix of a set of M mutually independent scalar time series. This matrix is composed of M2 blocks. Each block has size L×L and contains the sample crosscorrelation measured at L consecutive time lags between each pair of time series. Let N denote the total number of consecutively observed windows that are used to estimate

Partial isometries, duality, and determinantal point processes Random Matrices Theory Appl. (IF 0.9) Pub Date : 20211022
Makoto Katori, Tomoyuki ShiraiA determinantal point process (DPP) is an ensemble of random nonnegativeintegervalued Radon measures Ξ on a space S with measure λ, whose correlation functions are all given by determinants specified by an integral kernel K called the correlation kernel. We consider a pair of Hilbert spaces, Hℓ,ℓ=1,2, which are assumed to be realized as L2spaces, L2(Sℓ,λℓ), ℓ=1,2, and introduce a bounded linear

Random Toeplitz matrices: The condition number under high stochastic dependence Random Matrices Theory Appl. (IF 0.9) Pub Date : 20211022
Paulo ManriqueMirónIn this paper, we study the condition number of a random Toeplitz matrix. As a Toeplitz matrix is a diagonal constant matrix, its rows or columns cannot be stochastically independent. This situation does not permit us to use the classic strategies to analyze its minimum singular value when all the entries of a random matrix are stochastically independent. Using a circulant embedding as a decoupling

On the asymptotic behavior of the eigenvalue distribution of block correlation matrices of highdimensional time series Random Matrices Theory Appl. (IF 0.9) Pub Date : 20211022
Philippe Loubaton, Xavier MestreWe consider linear spectral statistics built from the blocknormalized correlation matrix of a set of M mutually independent scalar time series. This matrix is composed of M2 blocks. Each block has size L × L and contains the sample crosscorrelation measured at L consecutive time lags between each pair of time series. Let N denote the total number of consecutively observed windows that are used to

Partial isometries, duality, and determinantal point processes Random Matrices Theory Appl. (IF 0.9) Pub Date : 20211022
Makoto Katori, Tomoyuki ShiraiA determinantal point process (DPP) is an ensemble of random nonnegativeintegervalued Radon measures Ξ on a space S with measure λ, whose correlation functions are all given by determinants specified by an integral kernel K called the correlation kernel. We consider a pair of Hilbert spaces, Hℓ,ℓ = 1, 2, which are assumed to be realized as L2spaces, L2(S ℓ,λℓ), ℓ = 1, 2, and introduce a bounded

Random Toeplitz matrices: The condition number under high stochastic dependence Random Matrices Theory Appl. (IF 0.9) Pub Date : 20211022
Paulo ManriqueMirónIn this paper, we study the condition number of a random Toeplitz matrix. As a Toeplitz matrix is a diagonal constant matrix, its rows or columns cannot be stochastically independent. This situation does not permit us to use the classic strategies to analyze its minimum singular value when all the entries of a random matrix are stochastically independent. Using a circulant embedding as a decoupling

Spectral properties for the Laplacian of a generalized Wigner matrix Random Matrices Theory Appl. (IF 0.9) Pub Date : 20211014
Anirban Chatterjee, Rajat Subhra HazraIn this paper, we consider the spectrum of a Laplacian matrix, also known as Markov matrices where the entries of the matrix are independent but have a variance profile. Motivated by recent works on generalized Wigner matrices we assume that the variance profile gives rise to a sequence of graphons. Under the assumption that these graphons converge, we show that the limiting spectral distribution converges