Related papers: Estimates of norms of log-concave random matrices …

We prove estimates for the expected value of operator norms of Gaussian random matrices with independent and mean-zero entries, acting as operators from $\ell^m_{p^*}$ to $\ell_q^n$, $1\leq p^* \leq 2 \leq q \leq \infty$.

We prove a Chevet type inequality which gives an upper bound for the norm of an isotropic log-concave unconditional random matrix in terms of expectation of the supremum of "symmetric exponential" processes compared to the Gaussian ones in…

For $m,n\in\mathbb{N}$ let $X=(X_{ij})_{i\leq m,j\leq n}$ be a random matrix, $A=(a_{ij})_{i\leq m,j\leq n}$ a real deterministic matrix, and $X_A=(a_{ij}X_{ij})_{i\leq m,j\leq n}$ the corresponding structured random matrix. We study the…

We establish new tail estimates for order statistics and for the Euclidean norms of projections of an isotropic log-concave random vector. More generally, we prove tail estimates for the norms of projections of sums of independent…

Let $X$ be a symmetric, isotropic random vector in $\mathbb{R}^m$ and let $X_1...,X_n$ be independent copies of $X$. We show that under mild assumptions on $\|X\|_2$ (a suitable thin-shell bound) and on the tail-decay of the marginals…

In this paper, we consider the log-concave ensemble of random matrices, a class of covariance-type matrices $XX^*$ with isotropic log-concave $X$-columns. A main example is the covariance estimator of the uniform measure on isotropic convex…

We establish two-sided bounds for expectations of order statistics ($k$-th maxima) of moduli of coordinates of centered log-concave random vectors with uncorrelated coordinates. Our bounds are exact up to multiplicative universal constants…

We prove that for every $p,q\in[1,\infty]$ and every random matrix $X=(X_{i,j})_{i\le m, j\le n}$ with iid centered entries satisfying the regularity assumption $\|X_{i,j}\|_{2\rho} \le \alpha \|X_{i,j}\|_{\rho}$ for every $\rho \ge 1$, the…

In this note, we study the n x n random Euclidean matrix whose entry (i,j) is equal to f (|| Xi - Xj ||) for some function f and the Xi's are i.i.d. isotropic vectors in Rp. In the regime where n and p both grow to infinity and are…

We give estimates for the expectation of the norm of random matrices with independent but not necessarily identically distributed entries.

We prove concentration results for $\ell_p^n$ operator norms of rectangular random matrices and eigenvalues of self-adjoint random matrices. The random matrices we consider have bounded entries which are independent, up to a possible…

Let $\|A\|_{p,q}$ be the norm induced on the matrix $A$ with $n$ rows and $m$ columns by the H\"older $\ell_p$ and $\ell_q$ norms on $R^n$ and $R^m$ (or $C^n$ and $C^m$), respectively. It is easy to find an upper bound for the ratio…

We prove uniform estimates for the expected value of averages of order statistics of matrices in terms of their largest entries. As an application, we obtain similar probabilistic estimates for $\ell_p$ norms via real interpolation.

In this paper, we study the expectation of the operator norm of the random matrix (a_{ij} X_{ij}) for i,j <= n, under the assumption that the random variables (X_{ij}) are independent, symmetric and satisfy the moment growth condition…

We estimate the norms of standard Gaussian random Toeplitz and circulant matrices and their inverses, mostly by means of combining some basic techniques of linear algebra. In the case of circulant matrices we obtain sharp probabilistic…

We study approximation of the embedding $\ell_p^m \rightarrow \ell_{\infty}^m$, $1 \leq p \leq 2$, based on randomized adaptive algorithms that use arbitrary linear functionals as information on a problem instance. We show upper bounds for…

Let $A$ be an $N\times n$ random matrix whose entries are coordinates of an isotropic log-concave random vector in $\mathbb{R}^{Nn}$. We prove sharp lower tail estimates for the smallest singular value of $A$ in the following cases: (1)…

We derive two-sided bounds for moments of linear combinations of coordinates od unconditional log-concave vectors. We also investigate how well moments of such combinations may be approximated by moments of Gaussian random variables.

We consider nonnegative integer matrices with specified row and column sums and upper bounds on the entries. We show that the logarithm of the number of such matrices is approximated by a concave function of the row and column sums. We give…

Motivated by the Koml\'os conjecture in combinatorial discrepancy, we study the discrepancy of random matrices with $m$ rows and $n$ independent columns drawn from a bounded lattice random variable. It is known that for $n$ tending to…