Related papers: The Distribution of Permutation Matrix Entries Und…
We extend probability estimates on the smallest singular value of random matrices with independent entries to a class of sparse random matrices. We show that one can relax a previously used condition of uniform boundedness of the variances…
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted…
Random permutations with distribution conditionally uniform given the set of record values can be generated in a unified way, coherently for all values of $n$. Our central example is a two-parameter family of random permutations that are…
A truncation of a Haar distributed orthogonal random matrix gives rise to a matrix whose eigenvalues are either real or complex conjugate pairs, and are supported within the closed unit disk. This is also true for a product $P_m$ of $m$…
We are interested in two random matrix ensembles related to permutations: the ensemble of permutation matrices following Ewens' distribution of a given parameter $\theta >0$, and its modification where entries equal to $1$ in the matrices…
We provide an elementary proof for a theorem due to Petz and R\'effy which states that for a random $n\times n$ unitary matrix with distribution given by the Haar measure on the unitary group U(n), the upper left (or any other) $k\times k$…
We study random matrices with independent subgaussian columns. Assuming each column has a fixed Euclidean norm, we establish conditions under which such matrices act as near-isometries when restricted to a given subset of their domain. We…
Parametric distributions are an important part of statistics. There is now a voluminous literature on different fascinating formulations of flexible distributions. We present a selective and brief overview of a small subset of these…
A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…
We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new…
The present work provides an original framework for random matrix analysis based on revisiting the concentration of measure theory from a probabilistic point of view. By providing various notions of vector concentration ($q$-exponential,…
Using techniques from Poisson approximation, we prove explicit error bounds on the number of permutations that avoid any pattern. Most generally, we bound the total variation distance between the joint distribution of pattern occurrences…
We apply random matrix theory to complex networks. We show that nearest neighbor spacing distribution of the eigenvalues of the adjacency matrices of various model networks, namely scale-free, small-world and random networks follow…
Matrix-form Poisson probability distributions were recently introduced as one matrix generalization of Panjer distributions. We show in this paper that under the constraint that their representation is to be nonnegative, they have a…
When inferring parameters from a Gaussian-distributed data set by computing a likelihood, a covariance matrix is needed that describes the data errors and their correlations. If the covariance matrix is not known a priori, it may be…
This paper considers random (non-Hermitian) circulant matrices, and proves several results analogous to recent theorems on non-Hermitian random matrices with independent entries. In particular, the limiting spectral distribution of a random…
Some randomized algorithms, used to obtain a random $n^2 \times n^2$ Sudoku matrix, where $n$ is a natural number, is reviewed in this study. Below is described the set $\Pi_n$ of all $(2n) \times n$ matrices, consisting of elements of the…
We analyze the spectral distribution of symmetric random matrices with correlated entries. While we assume that the diagonals of these random matrices are stochastically independent, the elements of the diagonals are taken to be correlated.…
The paper gives a general condition on permutations, condition under which a semicircular matrix is free independent, or asymptotically free independent from the semicircular matrix obtained by permuting its entries. In particular, it is…
Recent theoretical studies of chaotic scattering have encounted ensembles of random matrices in which the eigenvalue probability density function contains a one-body factor with an exponent proportional to the number of eigenvalues. Two…