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Correction to: Speeding up Markov chains with deterministic jumps Probab Theory Relat Fields (IF 2.391) Pub Date : 20210906
Chatterjee, Sourav, Diaconis, PersiA correction to this paper has been published: https://doi.org/10.1007/s00440021010491

A formula for boundary correlations of the critical Ising model Probab Theory Relat Fields (IF 2.391) Pub Date : 20210826
Galashin, PavelGiven a finite rhombus tiling of a polygonal region in the plane, the associated critical Zinvariant Ising model is invariant under startriangle transformations. We give a simple matrix formula describing spin correlations between boundary vertices in terms of the shape of the region. When the region is a regular polygon, our formula becomes an explicit trigonometric sum.

Motion by mean curvature in interacting particle systems Probab Theory Relat Fields (IF 2.391) Pub Date : 20210825
Huang, Xiangying, Durrett, RickThere are a number of situations in which rescaled interacting particle systems have been shown to converge to a reaction diffusion equation (RDE) with a bistable reaction term, see e.g., Cox et al. (Astérisque 349:1–127, 2013), Durrett (Ann Appl Prob 19:477–496, 2009, Electron J Probab 19:1–64, 2014), Durrett and Neuhauser (Ann Probab 22:289–333, 1994). These RDEs have traveling wave solutions. When

Fluctuations of the loggamma polymer free energy with general parameters and slopes Probab Theory Relat Fields (IF 2.391) Pub Date : 20210825
Barraquand, Guillaume, Corwin, Ivan, Dimitrov, EvgeniWe prove that the free energy of the loggamma polymer between lattice points (1, 1) and (M, N) converges to the GUE Tracy–Widom distribution in the \(M^{1/3}\) scaling, provided that N/M remains bounded away from zero and infinity. We prove this result for the model with inverse gamma weights of any shape parameter \(\theta >0\) and furthermore establish a moderate deviation estimate for the upper

Harry Kesten’s work in probability theory Probab Theory Relat Fields (IF 2.391) Pub Date : 20210825
Grimmett, Geoffrey R.We survey the published work of Harry Kesten in probability theory, with emphasis on his contributions to random walks, branching processes, percolation, and related topics.

A spectral condition for spectral gap: fast mixing in hightemperature Ising models Probab Theory Relat Fields (IF 2.391) Pub Date : 20210820
Eldan, Ronen, Koehler, Frederic, Zeitouni, OferWe prove that Ising models on the hypercube with general quadratic interactions satisfy a Poincaré inequality with respect to the natural Dirichlet form corresponding to Glauber dynamics, as soon as the operator norm of the interaction matrix is smaller than 1. The inequality implies a control on the mixing time of the Glauber dynamics. Our techniques rely on a localization procedure which establishes

Poisson limit of bumping routes in the Robinson–Schensted correspondence Probab Theory Relat Fields (IF 2.391) Pub Date : 20210817
Marciniak, Mikołaj, Maślanka, Łukasz, Śniady, PiotrWe consider the Robinson–Schensted–Knuth algorithm applied to a random input and investigate the shape of the bumping route (in the vicinity of the yaxis) when a specified number is inserted into a large Planchereldistributed random tableau. We show that after a projective change of the coordinate system the bumping route converges in distribution to the Poisson process.

Quenched and averaged tails of the heat kernel of the twodimensional uniform spanning tree Probab Theory Relat Fields (IF 2.391) Pub Date : 20210804
Barlow, M. T., Croydon, D. A., Kumagai, T.This article investigates the heat kernel of the twodimensional uniform spanning tree. We improve previous work by demonstrating the occurrence of loglogarithmic fluctuations around the leading order polynomial behaviour for the ondiagonal part of the quenched heat kernel. In addition we give twosided estimates for the averaged heat kernel, and we show that the exponents that appear in the offdiagonal

Correction to: How linear reinforcement affects Donsker’s theorem for empirical processes Probab Theory Relat Fields (IF 2.391) Pub Date : 20210804
Bertoin, JeanA correction to this paper has been published: https://doi.org/10.1007/s00440021010482

Approximation of SDEs: a stochastic sewing approach Probab Theory Relat Fields (IF 2.391) Pub Date : 20210730
Butkovsky, Oleg, Dareiotis, Konstantinos, Gerencsér, MátéWe give a new take on the error analysis of approximations of stochastic differential equations (SDEs), utilizing and developing the stochastic sewing lemma of Lê (Electron J Probab 25:55, 2020. https://doi.org/10.1214/20EJP442). This approach allows one to exploit regularization by noise effects in obtaining convergence rates. In our first application we show convergence (to our knowledge for the

Nonuniformly parabolic equations and applications to the random conductance model Probab Theory Relat Fields (IF 2.391) Pub Date : 20210730
Bella, Peter, Schäffner, MathiasWe study local regularity properties of linear, nonuniformly parabolic finitedifference operators in divergence form related to the random conductance model on \(\mathbb Z^d\). In particular, we provide an oscillation decay assuming only certain summability properties of the conductances and their inverse, thus improving recent results in that direction. As an application, we provide a local limit

Scalar conservation laws with white noise initial data Probab Theory Relat Fields (IF 2.391) Pub Date : 20210724
Mehdi OuakiThe statistical description of the scalar conservation law of the form \(\rho _t=H(\rho )_x\) with \(H: {\mathbb {R}} \rightarrow {\mathbb {R}}\) a smooth convex function has been an object of interest when the initial profile \(\rho (\cdot ,0)\) is random. The special case when \(H(\rho )=\frac{\rho ^2}{2}\) (Burgers equation) has in particular received extensive interest in the past and is now understood

Convergence of the spectral radius of a random matrix through its characteristic polynomial Probab Theory Relat Fields (IF 2.391) Pub Date : 20210724
Charles Bordenave, Djalil Chafaï, David GarcíaZeladaConsider a square random matrix with independent and identically distributed entries of mean zero and unit variance. We show that as the dimension tends to infinity, the spectral radius is equivalent to the square root of the dimension in probability. This result can also be seen as the convergence of the support in the circular law theorem under optimal moment conditions. In the proof we establish

Anchored expansion of Delaunay complexes in real hyperbolic space and stationary point processes Probab Theory Relat Fields (IF 2.391) Pub Date : 20210723
Itai Benjamini, Yoav Krauz, Elliot PaquetteWe give sufficient conditions for a discrete set of points in any dimensional real hyperbolic space to have positive anchored expansion. The first condition is an anchored bounded density property, ensuring not too many points can accumulate in large regions. The second is an anchored bounded vacancy condition, effectively ensuring there is not too much space left vacant by the points over large regions

Limits of multiplicative inhomogeneous random graphs and Lévy trees: limit theorems Probab Theory Relat Fields (IF 2.391) Pub Date : 20210718
Nicolas Broutin, Thomas Duquesne, Minmin WangWe consider a natural model of inhomogeneous random graphs that extends the classical Erdős–Rényi graphs and shares a close connection with the multiplicative coalescence, as pointed out by Aldous (Ann Probab 25:812–854, 1997). In this model, the vertices are assigned weights that govern their tendency to form edges. It is by looking at the asymptotic distributions of the masses (sum of the weights)

Limit profiles for reversible Markov chains Probab Theory Relat Fields (IF 2.391) Pub Date : 20210714
Evita Nestoridi, Sam OleskerTaylorIn a recent breakthrough, Teyssier (Ann Probab 48(5):2323–2343, 2020) introduced a new method for approximating the distance from equilibrium of a random walk on a group. He used it to study the limit profile for the random transpositions card shuffle. His techniques were restricted to conjugacyinvariant random walks on groups; we derive similar approximation lemmas for random walks on homogeneous

Quenched invariance principle for a class of random conductance models with longrange jumps Probab Theory Relat Fields (IF 2.391) Pub Date : 20210713
Marek Biskup, Xin Chen, Takashi Kumagai, Jian WangWe study random walks on \({\mathbb {Z}}^d\) (with \(d\ge 2\)) among stationary ergodic random conductances \(\{C_{x,y}:x,y\in {\mathbb {Z}}^d\}\) that permit jumps of arbitrary length. Our focus is on the quenched invariance principle (QIP) which we establish by a combination of corrector methods, functional inequalities and heatkernel technology assuming that the pth moment of \(\sum _{x\in {\mathbb

Mapping TASEP back in time Probab Theory Relat Fields (IF 2.391) Pub Date : 20210709
Leonid Petrov, Axel SaenzWe obtain a new relation between the distributions \(\upmu _t\) at different times \(t\ge 0\) of the continuoustime totally asymmetric simple exclusion process (TASEP) started from the step initial configuration. Namely, we present a continuoustime Markov process with local interactions and particledependent rates which maps the TASEP distributions \(\upmu _t\) backwards in time. Under the backwards

Spine representations for noncompact models of random geometry Probab Theory Relat Fields (IF 2.391) Pub Date : 20210705
JeanFrançois Le Gall, Armand RieraWe provide a unified approach to the three main noncompact models of random geometry, namely the Brownian plane, the infinitevolume Brownian disk, and the Brownian halfplane. This approach allows us to investigate relations between these models, and in particular to prove that complements of hulls in the Brownian plane are infinitevolume Brownian disks.

Nonsimple conformal loop ensembles on Liouville quantum gravity and the law of CLE percolation interfaces Probab Theory Relat Fields (IF 2.391) Pub Date : 20210626
Jason Miller, Scott Sheffield, Wendelin WernerWe study the structure of the Liouville quantum gravity (LQG) surfaces that are cut out as one explores a conformal loopensemble \(\hbox {CLE}_{\kappa '}\) for \(\kappa '\) in (4, 8) that is drawn on an independent \(\gamma \)LQG surface for \(\gamma ^2=16/\kappa '\). The results are similar in flavor to the ones from our companion paper dealing with \(\hbox {CLE}_{\kappa }\) for \(\kappa \) in (8/3

Isoperimetric profiles and random walks on some groups defined by piecewise actions Probab Theory Relat Fields (IF 2.391) Pub Date : 20210624
Laurent SaloffCoste, Tianyi ZhengWe study the isoperimetric and spectral profiles of certain families of finitely generated groups defined via actions on labelled Schreier graphs and simple gluing of such. In one of our simplest constructions—the pocketextension of a group G—this leads to the study of certain finitely generated subgroups of the full permutation group \({\mathbb {S}}(G\cup \{*\})\). Some sharp estimates are obtained

The local limit of uniform spanning trees Probab Theory Relat Fields (IF 2.391) Pub Date : 20210622
Asaf Nachmias, Yuval PeresWe show that the local limit of the uniform spanning tree on any finite, simple, connected, regular graph sequence with degree tending to \(\infty \) is the Poisson(1) branching process conditioned to survive forever. An extension to “almost” regular graphs and a quenched version are also given.

Planar randomcluster model: fractal properties of the critical phase Probab Theory Relat Fields (IF 2.391) Pub Date : 20210619
Hugo DuminilCopin, Ioan Manolescu, Vincent TassionThis paper is studying the critical regime of the planar randomcluster model on \({\mathbb {Z}}^2\) with clusterweight \(q\in [1,4)\). More precisely, we prove crossing estimates in quads which are uniform in their boundary conditions and depend only on their extremal lengths. They imply in particular that any fractal boundary is touched by macroscopic clusters, uniformly in its roughness or the

Geometry of the minimal spanning tree of a random 3regular graph Probab Theory Relat Fields (IF 2.391) Pub Date : 20210612
Louigi AddarioBerry, Sanchayan SenThe global structure of the minimal spanning tree (MST) is expected to be universal for a large class of underlying random discrete structures. However, very little is known about the intrinsic geometry of MSTs of most standard models, and so far the scaling limit of the MST viewed as a metric measure space has only been identified in the case of the complete graph (AddarioBerry et al. in Ann Probab

Phase transitions for spatially extended pinning Probab Theory Relat Fields (IF 2.391) Pub Date : 20210609
Francesco Caravenna, Frank den HollanderWe consider a directed polymer of length N interacting with a linear interface. The monomers carry i.i.d. random charges \((\omega _i)_{i=1}^N\) taking values in \({\mathbb {R}}\) with mean zero and variance one. Each monomer i contributes an energy \((\beta \omega _ih)\varphi (S_i)\) to the interaction Hamiltonian, where \(S_i \in {\mathbb {Z}}\) is the height of monomer i with respect to the interface

Powerlaw bounds for critical longrange percolation below the uppercritical dimension Probab Theory Relat Fields (IF 2.391) Pub Date : 20210608
Tom HutchcroftWe study longrange Bernoulli percolation on \({\mathbb {Z}}^d\) in which each two vertices x and y are connected by an edge with probability \(1\exp (\beta \Vert xy\Vert ^{d\alpha })\). It is a theorem of Noam Berger (Commun. Math. Phys., 2002) that if \(0<\alpha

Tests and estimation strategies associated to some loss functions Probab Theory Relat Fields (IF 2.391) Pub Date : 20210606
Yannick BaraudWe consider the problem of estimating the joint distribution of n independent random variables. Given a loss function and a family of candidate probabilities, that we shall call a model, we aim at designing an estimator with values in our model that possesses good estimation properties not only when the distribution of the data belongs to the model but also when it lies close enough to it. The losses

Persistence of hubs in growing random networks Probab Theory Relat Fields (IF 2.391) Pub Date : 20210531
Sayan Banerjee, Shankar BhamidiWe consider models of evolving networks \(\left\{ {\mathcal {G}}_n:n\ge 0\right\} \) modulated by two parameters: an attachment function \(f:{\mathbb {N}}_0 \rightarrow {\mathbb {R}}_+\) and a (possibly random) attachment sequence \(\left\{ m_i:i\ge 1\right\} \). Starting with a single vertex, at each discrete step \(i\ge 1\) a new vertex \(v_i\) enters the system with \(m_i\ge 1\) edges which it sequentially

Scaling limits of multitype Markov Branching trees Probab Theory Relat Fields (IF 2.391) Pub Date : 20210531
Bénédicte Haas, Robin StephensonWe introduce multitype Markov Branching trees, which are simple random population tree models where individuals are characterized by their size and their type and give rise to (size,type)children in a Galton–Watson fashion, with the rule that the size of any individual is at least the sum of the sizes of its children. Assuming that the macroscopic sizesplittings are rare, we describe the scaling

Eigenvector distribution in the critical regime of BBP transition Probab Theory Relat Fields (IF 2.391) Pub Date : 20210531
Zhigang Bao, Dong WangIn this paper, we study the random matrix model of Gaussian Unitary Ensemble (GUE) with fixedrank (aka spiked) external source. We will focus on the critical regime of the Baik–Ben Arous–Péché (BBP) phase transition and establish the distribution of the eigenvectors associated with the leading eigenvalues. The distribution is given in terms of a determinantal point process with extended Airy kernel

Liouville dynamical percolation Probab Theory Relat Fields (IF 2.391) Pub Date : 20210529
Christophe Garban, Nina Holden, Avelio Sepúlveda, Xin SunWe construct and analyze a continuum dynamical percolation process which evolves in a random environment given by a \(\gamma \)Liouville measure. The homogeneous counterpart of this process describes the scaling limit of discrete dynamical percolation on the rescaled triangular lattice. Our focus here is to study the same limiting dynamics, but where the speed of microscopic updates is highly inhomogeneous

On planar graphs of uniform polynomial growth Probab Theory Relat Fields (IF 2.391) Pub Date : 20210527
Farzam Ebrahimnejad, James R. LeeConsider an infinite planar graph with uniform polynomial growth of degree \(d > 2\). Many examples of such graphs exhibit similar geometric and spectral properties, and it has been conjectured that this is necessary. We present a family of counterexamples. In particular, we show that for every rational \(d > 2\), there is a planar graph with uniform polynomial growth of degree d on which the random

The two regimes of moderate deviations for the range of a transient walk Probab Theory Relat Fields (IF 2.391) Pub Date : 20210512
Amine Asselah, Bruno SchapiraWe obtain sharp upper and lower bounds for the downward moderate deviations of the volume of the range of a random walk in dimension five and larger. Our results encompass two regimes: a Gaussian regime for small deviations, and a stretched exponential regime for larger deviations. In the latter regime, we show that conditioned on the moderate deviations event, the walk folds a small part of its range

An emergent autonomous flow for meanfield spin glasses Probab Theory Relat Fields (IF 2.391) Pub Date : 20210507
James MacLaurinWe study the dynamics of symmetric and asymmetric spinglass models of size N. The analysis is in terms of the double empirical process: this contains both the spins, and the field felt by each spin, at a particular time (without any knowledge of the correlation history). It is demonstrated that in the large N limit, the dynamics of the double empirical process becomes deterministic and autonomous

A free boundary characterisation of the Root barrier for Markov processes Probab Theory Relat Fields (IF 2.391) Pub Date : 20210506
Paul Gassiat, Harald Oberhauser, Christina Z. ZouWe study the existence, optimality, and construction of nonrandomised stopping times that solve the Skorokhod embedding problem (SEP) for Markov processes which satisfy a duality assumption. These stopping times are hitting times of spacetime subsets, socalled Root barriers. Our main result is, besides the existence and optimality, a potentialtheoretic characterisation of this Root barrier as a

Convergence of random walks with Markovian cookie stacks to Brownian motion perturbed at extrema Probab Theory Relat Fields (IF 2.391) Pub Date : 20210506
Elena Kosygina, Thomas Mountford, Jonathon PetersonWe consider onedimensional excited random walks (ERWs) with i.i.d. Markovian cookie stacks in the nonboundary recurrent regime. We prove that under diffusive scaling such an ERW converges in the standard Skorokhod topology to a multiple of Brownian motion perturbed at its extrema (BMPE). All parameters of the limiting process are given explicitly in terms of those of the cookie Markov chain at a

Regularity of SLE in $$(t,\kappa )$$ ( t , κ ) and refined GRR estimates Probab Theory Relat Fields (IF 2.391) Pub Date : 20210506
Peter K. Friz, Huy Tran, Yizheng YuanSchramm–Loewner evolution (\(\hbox {SLE}_\kappa \)) is classically studied via Loewner evolution with halfplane capacity parametrization, driven by \(\sqrt{\kappa }\) times Brownian motion. This yields a (halfplane) valued random field \(\gamma = \gamma (t, \kappa ; \omega )\). (Hölder) regularity of in \(\gamma (\cdot ,\kappa ;\omega \)), a.k.a. SLE trace, has been considered by many authors, starting

A transportation approach to the meanfield approximation Probab Theory Relat Fields (IF 2.391) Pub Date : 20210503
Fanny AugeriWe develop transportationentropy inequalities which are saturated by measures such that their logdensity with respect to the background measure is an affine function, in the setting of the uniform measure on the discrete hypercube and the exponential measure. In this sense, this extends the wellknown result of Talagrand in the Gaussian case. By duality, these transportationentropy inequalities

Nsided radial Schramm–Loewner evolution Probab Theory Relat Fields (IF 2.391) Pub Date : 20210428
Vivian Olsiewski Healey, Gregory F. LawlerWe use the interpretation of the Schramm–Loewner evolution as a limit of path measures tilted by a loop term in order to motivate the definition of nradial SLE going to a particular point. In order to justify the definition we prove that the measure obtained by an appropriately normalized loop term on ntuples of paths has a limit. The limit measure can be described as n paths moving by the Loewner

Exponential decay of transverse correlations for O ( N ) spin systems and related models Probab Theory Relat Fields (IF 2.391) Pub Date : 20210428
Benjamin Lees, Lorenzo TaggiWe prove exponential decay of transverse correlations in the Spin O(N) model for arbitrary nonzero values of the external magnetic field and arbitrary spin dimension \(N > 1\). Our result is new when \(N > 3\), in which case no Lee–Yang theorem is available, it is an alternative to Lee–Yang when \(N = 2, 3\), and also holds for a wide class of multicomponent spin systems with continuous symmetry

Fluctuations of extreme eigenvalues of sparse Erdős–Rényi graphs Probab Theory Relat Fields (IF 2.391) Pub Date : 20210424
Yukun He, Antti KnowlesWe consider a class of sparse random matrices which includes the adjacency matrix of the Erdős–Rényi graph \({{\mathcal {G}}}(N,p)\). We show that if \(N^{\varepsilon } \leqslant Np \leqslant N^{1/3\varepsilon }\) then all nontrivial eigenvalues away from 0 have asymptotically Gaussian fluctuations. These fluctuations are governed by a single random variable, which has the interpretation of the total

Critical Brownian multiplicative chaos Probab Theory Relat Fields (IF 2.391) Pub Date : 20210409
Antoine JegoBrownian multiplicative chaos measures, introduced in Jego (Ann Probab 48:1597–1643, 2020), Aïdékon et al. (Ann Probab 48(4):1785–1825, 2020) and Bass et al. (Ann Probab 22:566–625, 1994), are random Borel measures that can be formally defined by exponentiating \(\gamma \) times the square root of the local times of planar Brownian motion. So far, only the subcritical measures where the parameter \(\gamma

Planarity and nonseparating cycles in uniform high genus quadrangulations Probab Theory Relat Fields (IF 2.391) Pub Date : 20210405
Baptiste LoufWe study large uniform random bipartite quadrangulations whose genus grows linearly with the number of faces. Their local convergence was recently established by Budzinski and the author [9, 10]. Here we study several properties of these objects which are not captured by the local topology. Namely we show that balls around the root are planar with high probability up to logarithmic radius, and we prove

The effect of free boundary conditions on the Ising model in high dimensions Probab Theory Relat Fields (IF 2.391) Pub Date : 20210331
Federico Camia, Jianping Jiang, Charles M. NewmanWe study the critical Ising model with free boundary conditions on finite domains in \({\mathbb {Z}}^d\) with \(d\ge 4\). Under the assumption, so far only proved completely for high d, that the critical infinite volume twopoint function is of order \(xy^{(d2)}\) for large \(xy\), we prove the same is valid on large finite cubes with free boundary conditions, as long as x, y are not too close

Nearcritical 2D percolation with heavytailed impurities, forest fires and frozen percolation Probab Theory Relat Fields (IF 2.391) Pub Date : 20210331
Jacob van den Berg, Pierre NolinWe introduce a new percolation model on planar lattices. First, impurities (“holes”) are removed independently from the lattice. On the remaining part, we then consider site percolation with some parameter p close to the critical value \(p_c\). The mentioned impurities are not only microscopic, but allowed to be mesoscopic (“heavytailed”, in some sense). For technical reasons (the proofs of our results

Nonparametric estimation for interacting particle systems: McKean–Vlasov models Probab Theory Relat Fields (IF 2.391) Pub Date : 20210330
Laetitia Della Maestra, Marc HoffmannWe consider a system of N interacting particles, governed by transport and diffusion, that converges in a meanfield limit to the solution of a McKean–Vlasov equation. From the observation of a trajectory of the system over a fixed time horizon, we investigate nonparametric estimation of the solution of the associated nonlinear Fokker–Planck equation, together with the drift term that controls the

Liouville quantum gravity and the Brownian map III: the conformal structure is determined Probab Theory Relat Fields (IF 2.391) Pub Date : 20210325
Jason Miller, Scott SheffieldPrevious works in this series have shown that an instance of a \(\sqrt{8/3}\)Liouville quantum gravity (LQG) sphere has a welldefined distance function, and that the resulting metric measure space (mmspace) agrees in law with the Brownian map (TBM). In this work, we show that given just the mmspace structure, one can a.s. recover the LQG sphere. This implies that there is a canonical way to parameterize

Does a central limit theorem hold for the k skeleton of Poisson hyperplanes in hyperbolic space? Probab Theory Relat Fields (IF 2.391) Pub Date : 20210321
Felix Herold, Daniel Hug, Christoph ThälePoisson processes in the space of \((d1)\)dimensional totally geodesic subspaces (hyperplanes) in a ddimensional hyperbolic space of constant curvature \(1\) are studied. The kdimensional Hausdorff measure of their kskeleton is considered. Explicit formulas for first and secondorder quantities restricted to bounded observation windows are obtained. The central limit problem for the kdimensional

On the maximal displacement of nearcritical branching random walks Probab Theory Relat Fields (IF 2.391) Pub Date : 20210320
Eyal Neuman, Xinghua ZhengWe consider a branching random walk on \(\mathbb {Z}\) started by n particles at the origin, where each particle disperses according to a meanzero random walk with bounded support and reproduces with mean number of offspring \(1+\theta /n\). For \(t\ge 0\), we study \(M_{nt}\), the rightmost position reached by the branching random walk up to generation [nt]. Under certain moment assumptions on the

Local stationarity in exponential lastpassage percolation Probab Theory Relat Fields (IF 2.391) Pub Date : 20210315
Márton Balázs, Ofer Busani, Timo SeppäläinenWe consider pointtopoint lastpassage times to every vertex in a neighbourhood of size \(\delta N^{\nicefrac {2}{3}}\) at distance N from the starting point. The increments of the lastpassage times in this neighbourhood are shown to be jointly equal to their stationary versions with high probability that depends only on \(\delta \). Through this result we show that (1) the \(\text {Airy}_2\) process

Interacting diffusions on positive definite matrices Probab Theory Relat Fields (IF 2.391) Pub Date : 20210315
Neil O’ConnellWe consider systems of Brownian particles in the space of positive definite matrices, which evolve independently apart from some simple interactions. We give examples of such processes which have an integrable structure. These are related to KBessel functions of matrix argument and multivariate generalisations of these functions. The latter are eigenfunctions of a particular quantisation of the nonAbelian

Sharp transition of the invertibility of the adjacency matrices of sparse random graphs Probab Theory Relat Fields (IF 2.391) Pub Date : 20210313
Anirban Basak, Mark RudelsonWe consider three models of sparse random graphs: undirected and directed Erdős–Rényi graphs and random bipartite graph with two equal parts. For such graphs, we show that if the edge connectivity probability p satisfies \(np\ge \log n+k(n)\) with \(k(n)\rightarrow \infty \) as \(n\rightarrow \infty \), then the adjacency matrix is invertible with probability approaching one (n is the number of vertices

The bead process for beta ensembles Probab Theory Relat Fields (IF 2.391) Pub Date : 20210313
Joseph Najnudel, Bálint VirágThe bead process introduced by Boutillier is a countable interlacing of the \({\text {Sine}}_2\) point processes. We construct the bead process for general \({\text {Sine}}_{\beta }\) processes as an infinite dimensional Markov chain whose transition mechanism is explicitly described. We show that this process is the microscopic scaling limit in the bulk of the Hermite \(\beta \) corner process introduced

High mode transport noise improves vorticity blowup control in 3D Navier–Stokes equations Probab Theory Relat Fields (IF 2.391) Pub Date : 20210310
Franco Flandoli, Dejun LuoThe paper is concerned with the problem of regularization by noise of 3D Navier–Stokes equations. As opposed to several attempts made with additive noise which remained inconclusive, we show here that a suitable multiplicative noise of transport type has a regularizing effect. It is proven that stochastic transport noise provides a bound on vorticity which gives well posedness, with high probability

Second time scale of the metastability of reversible inclusion processes Probab Theory Relat Fields (IF 2.391) Pub Date : 20210307
Seonwoo KimWe investigate the second time scale of the metastable behavior of the reversible inclusion process in an extension of the study by Bianchi et al. (Electron J Probab 22:1–34, 2017), which presented the first time scale of the same model and conjectured the scheme of multiple time scales. We show that \(N/d_{N}^{2}\) is indeed the correct second time scale for the most general class of reversible inclusion

Quenched local limit theorem for random walks among timedependent ergodic degenerate weights Probab Theory Relat Fields (IF 2.391) Pub Date : 20210304
Sebastian Andres, Alberto Chiarini, Martin SlowikWe establish a quenched local central limit theorem for the dynamic random conductance model on \({\mathbb {Z}}^d\) only assuming ergodicity with respect to spacetime shifts and a moment condition. As a key analytic ingredient we show Hölder continuity estimates for solutions to the heat equation for discrete finite difference operators in divergence form with timedependent degenerate weights. The

KMT coupling for random walk bridges Probab Theory Relat Fields (IF 2.391) Pub Date : 20210302
Evgeni Dimitrov, Xuan WuIn this paper we prove an analogue of the Komlós–Major–Tusnády (KMT) embedding theorem for random walk bridges. The random bridges we consider are constructed through random walks with i.i.d jumps that are conditioned on the locations of their endpoints. We prove that such bridges can be strongly coupled to Brownian bridges of appropriate variance when the jumps are either continuous or integer valued

A planar Ising model of selforganized criticality Probab Theory Relat Fields (IF 2.391) Pub Date : 20210212
Nicolas ForienWe consider the planar Ising model in a finite square box and we replace the temperature parameter with a function depending on the magnetization. This creates a feedback from the spin configuration onto the parameter, which drives the system towards the critical point. Using the finitesize scaling results of Cerf and Messikh (Theory Relat Fields 150(1–2):193–217, 2011. https://doi.org/10.1007/s0044001002720)

The band structure of a model of spatial random permutation Probab Theory Relat Fields (IF 2.391) Pub Date : 20210207
Yan V. Fyodorov, Stephen MuirheadWe study a random permutation of a lattice box in which each permutation is given a Boltzmann weight with energy equal to the total Euclidean displacement. Our main result establishes the band structure of the model as the boxsize N tends to infinity and the inverse temperature \(\beta \) tends to zero; in particular, we show that the mean displacement is of order \(\min \{1/\beta , N\}\). In one

Phase transitions for a class of gradient fields Probab Theory Relat Fields (IF 2.391) Pub Date : 20210206
Simon BuchholzWe consider gradient fields on \({\mathbb {Z}}^d\) for potentials V that can be expressed as $$\begin{aligned} e^{V(x)}=pe^{\frac{qx^2}{2}}+(1p)e^{\frac{x^2}{2}}. \end{aligned}$$ This representation allows us to associate a random conductance type model to the gradient fields with zero tilt. We investigate this random conductance model and prove correlation inequalities, duality properties, and