Related papers: Subgaussianity is hereditarily determined

Random models of evolution are instrumental in extracting rates of microscopic evolutionary mechanisms from empirical observations on genetic variation in genome sequences. In this context it is necessary to know the statistical properties…

Let $\{X, X_n, n\geq 1\}$ be a sequence of independent identically distributed non-degenerate random variables. Put $S_0=0, S_n = \sum^n_{i=1} X_i$ and $V_n^2=\sum^n_{i=1} X_i^2, n\ge 1.$ A weak convergence theorem is established for the…

Let $\mathcal{F}$ be a collection of $r$-uniform hypergraphs, and let $0 < p < 1$. It is known that there exists $c = c(p,\mathcal{F})$ such that the probability of a random $r$-graph in $G(n,p)$ not containing an induced subgraph from…

Finite sample properties of random covariance-type matrices have been the subject of much research. In this paper we focus on the "lower tail" of such a matrix, and prove that it is subgaussian under a simple fourth moment assumption on the…

The determinant of the Gaussian unitary ensemble matrix is show to be distributed as a product of independent chi random variables with parameters $1,3,3,5,5,\dots.$

Let $X_{1}=(W_{1},Y_{1}),\ldots,X_{n}=(W_{n},Y_{n})$ be $n$ pairs of independent random variables. We assume that, for each $i\in\{1,\ldots,n\}$, the conditional distribution of $Y_{i}$ given $W_{i}$ belongs to a one-parameter exponential…

Let $\varepsilon_1,\ldots,\varepsilon_n$ be independent identically distributed Rademacher random variables, that is $\mathbb{P}\{\varepsilon_i=\pm1\}=1/2$. Let $S_n=a_1\varepsilon_1+\cdots+a_n\varepsilon_n$, where…

It is proved that the limiting distribution of the length of the longest weakly increasing subsequence in an inhomogeneous random word is related to the distribution function for the eigenvalues of a certain direct sum of Gaussian unitary…

Let $\{X_t, t \geq 1\}$ be a sequence of identically distributed and pairwise asymptotically independent random variables with regularly varying tails and $\{ \Theta_t, t\geq1 \}$ be a sequence of positive random variables independent of…

In this paper, we study the subgaussian matrix variate model, where we observe the matrix variate data $X$ which consists of a signal matrix $X_0$ and a noise matrix $W$. More specifically, we study a subgaussian model using the Kronecker…

Let $\{X_i,i\geq1\}$ be a sequence of negatively associated random variables, and let $\{X_i^\ast,i\geq 1\}$ be a sequence of independent random variables such that $X_i^\ast$ and $X_i$ have the same distribution for each $i$. Denote by…

We consider eigenvectors of the Hamiltonian $H_0$ perturbed by a generic perturbation $V$ modelled by a random matrix from the Gaussian Unitary Ensemble (GUE). Using the supersymmetry approach we derive analytical results for the statistics…

We consider the following detection problem: given a realization of a symmetric matrix ${\mathbf{X}}$ of dimension $n$, distinguish between the hypothesis that all upper triangular variables are i.i.d. Gaussians variables with mean 0 and…

Let $Y$ be a Gaussian vector of $\mathbb{R}^n$ of mean $s$ and diagonal covariance matrix $\Gamma$. Our aim is to estimate both $s$ and the entries $\sigma_i=\Gamma_{i,i}$, for $i=1,...,n$, on the basis of the observation of two independent…

Given $n$ positive integers $a_1,a_2,\dots,a_n$, and a positive integer right hand side $\beta$, we consider the feasibility version of the subset sum problem which is the problem of determining whether a subset of $a_1,a_2,\dots,a_n$ adds…

Under certain conditions on k we calculate the limit distribution of the k:th largest eigenvalue, x_k, of the Gaussian Unitary Ensemble (GUE). More specifically, if n is the dimension of a random matrix from the GUE and k is such that both…

The aim of this paper is to give a precise asymptotic description of some eigenvalue statistics stemming from random matrix theory. More precisely, we consider random determinants of the GUE, Laguerre, Uniform Gram and Jacobi beta ensembles…

Let $X_1,X_2,...$ be independent variables, each having a normal distribution with negative mean $-\beta<0$ and variance 1. We consider the partial sums $S_n=X_1+...+X_n$, with $S_0=0$, and refer to the process $\{S_n:n\geq0\}$ as the…

We consider the following data perturbation model, where the covariates incur multiplicative errors. For two $n \times m$ random matrices $U, X$, we denote by $U \circ X$ the Hadamard or Schur product, which is defined as $(U \circ X)_{ij}…

This paper establishes the optimal sub-Gaussian variance proxy for truncated Gaussian and truncated exponential random variables. The proofs rely on first characterizing the optimal variance proxy as the unique solution to a set of two…