相关论文: Classical and free infinitely divisible distributi…
In this paper the question about statistical properties of block--hierarchical random matrices is raised for the first time in connection with structural characteristics of random hierarchical networks obtained by mipmapping procedure. In…
We show that the averaged characteristic polynomial and the averaged inverse characteristic polynomial, associated with Hermitian matrices whose elements perform a random walk in the space of complex numbers, satisfy certain partial…
Fix a partition $\mu=(\mu_1,\dotsc,\mu_m)$ of an integer $k$ and positive integer $d$. For each $n>k$, let $\chi^\lambda_\mu$ denote the value of the irreducible character of $S_n$ at a permutation with cycle type…
This paper studies new classes of infinitely divisible distributions on R^d. Firstly, the connecting classes with a continuous parameter between the Jurek class and the class of selfdecomposable distributions are revisited. Secondly, the…
We introduce a complex-plane generalization of the consecutive level-spacing distribution, used to distinguish regular from chaotic quantum spectra. Our approach features the distribution of complex-valued ratios between nearest- and…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions are a special case where the density matrix is restricted to be diagonal. Density…
Consider 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…
It has been shown by Voiculescu that important classes of square independent random matrices are asymptotically free, where freeness is a noncommutative analog of classical independence. Recently, we introduced the concept of matricial…
A large i.i.d. random matrix with deterministic low-rank perturbation has been extensively studied, particularly in the aspects of the ESD (Empirical Spectral Distribution) and the outliers of eigenvalues. In this work, we investigate the…
We investigate traces of powers of random matrices whose distributions are invariant under rotations (with respect to the Hilbert--Schmidt inner product) within a real-linear subspace of the space of $n\times n$ matrices. The matrices we…
We analyze the spectral properties of the high-dimensional random geometric graph $G(n, d, p)$, formed by sampling $n$ i.i.d vectors $\{v_i\}_{i=1}^{n}$ uniformly on a $d$-dimensional unit sphere and connecting each pair $\{i,j\}$ whenever…
We consider a parameter dependent ensemble of two real random matrices with Gaussian distribution. It describes the transition between the symmetry class of the chiral Gaussian orthogonal ensemble (Cartan class B$|$DI) and the ensemble of…
It is known that the empirical spectral distribution of random matrices obtained from linear codes of increasing length converges to the well-known Marchenko-Pastur law, if the Hamming distance of the dual codes is at least 5. In this…
Classical random matrix ensembles with orthogonal symmetry have the property that the joint distribution of every second eigenvalue is equal to that of a classical random matrix ensemble with symplectic symmetry. These results are shown to…
Let $\mathbf X=(X_{jk})_{j,k=1}^n$ denote a Hermitian random matrix with entries $X_{jk}$, which are independent for $1\le j\le k\le n$. We consider the rate of convergence of the empirical spectral distribution function of the matrix…
An elliptic random matrix $X$ is a square matrix whose $(i,j)$-entry $X_{ij}$ is independent of the rest of the entries except possibly $X_{ji}$. Elliptic random matrices generalize Wigner matrices and non-Hermitian random matrices with…
Spectral properties of Hermitian Toeplitz, Hankel, and Toeplitz-plus-Hankel random matrices with independent identically distributed entries are investigated. Combining numerical and analytic arguments it is demonstrated that spectral…
The goal of this paper is to show how different machine learning tools on the Riemannian manifold $\mathcal{P}_d$ of Symmetric Positive Definite (SPD) matrices can be united under a probabilistic framework. For this, we will need several…
The one-dimensional Dickman distribution arises in various stochastic models across number theory, combinatorics, physics, and biology. Recently, a definition of the multidimensional Dickman distribution has appeared in the literature,…
The study of a particle with position-dependent effective mass (pdem), within a double heterojunction is extended into the complex domain --- when the region within the heterojunctions is described by a non Hermitian ${\cal{PT}}$ symmetric…