In this paper, we study the probability distribution of eigenvalues of the $n\times n$ Euclidean random matrix whose $(i,j{)}^{th}$ entry is of the form $f(\parallel {\mathbf{x}}_i-{\mathbf{x}}_j{\parallel }^2)-u_n{\delta }_{ij}\sum _{k}f(\parallel {\mathbf{x}}_i-{\mathbf{x}}_k{\parallel }^2)$ for some real function f. Random points $x_i$'s are independently distributed in the $l_p$ ellipsoid or on its surface in ${\mathbb{R}}^N$ including the unit sphere $S^{N-1}$, the simplex, the ordinary ellipsoid and the hyper-cube. Here $u_n$ is allowed to be any real number which includes the two most interesting cases $u_n=0$ and $u_n=1$. The limits of the empirical distribution of its eigenvalues are derived in two high dimensional settings: $n/N\to \gamma \in (0,\mathrm{\infty })$ and $n/N\to 0$ as both n and N go to infinity. By taking $f\left(x\right)$ to be suitable functions, we also give the explicit limiting spectral distributions for some distance matrices whose entries are based on the Euclidean distance and the geodesic distance.

在本文中，我们研究了特征值的概率分布$n\times n$欧几里得随机矩阵$(\mathrm{一世},j{)}^{吨H}$条目的形式$F(\parallel {\mathbf{X}}_{\mathrm{一世}}-{\mathbf{X}}_j{\parallel }^2)-{你}_n{\delta }_{\mathrm{一世}j}\sum _{ķ}F(\parallel {\mathbf{X}}_{\mathrm{一世}}-{\mathbf{X}}_{ķ}{\parallel }^2)$对于一些实函数f。随机点$X_{\mathrm{一世}}$的独立分布在$l_p$椭球体或其表面上${\mathbb{R}}^{ñ}$包括单位球体${\mathrm{小号}}^{ñ-1}$、单纯形、普通椭球和超立方体。这里${你}_n$允许是任何实数，包括两个最有趣的情况${你}_n=0$和${你}_n=1$. 其特征值的经验分布的极限是在两个高维设置中得出的：$n/ñ\to \gamma \in (0,\mathrm{\infty })$和$n/ñ\to 0$因为n和N都趋于无穷大。通过采取$F\left(X\right)$为了成为合适的函数，我们还给出了一些距离矩阵的显式限制谱分布，这些距离矩阵的条目基于欧几里得距离和测地线距离。