Related papers: Norms of structured random matrices

We prove a stability version of a general result that bounds the permanent of a matrix in terms of its operator norm. More specifically, suppose $A$ is an $n \times n$ matrix over $\mathbb{C}$ (resp. $\mathbb{R}$), and let $\mathcal{P}$…

In the paper I study properties of random polynomials with respect to a general system of functions. Some lower bounds for the mathematical expectation of the uniform and recently introduced integral-uniform norms of random polynomials are…

We present a brief introduction to the theory of operator limits of random matrices to non-experts. Several open problems and conjectures are given. Connections to statistics, integrable systems, orthogonal polynomials, and more, are…

Given a structured matrix $A$ we study the problem of finding the closest normal matrix with the same structure. The structures of our interest are: Hamiltonian, skew-Hamiltonian, per-Hermitian, and perskew-Hermitian. We develop a…

In this note, we show that the norm of an $n\times n$ random jointly exchangeable matrix with zero diagonal can be estimated in terms of the norm of its $n/2\times n/2$ submatrix located in the top right corner. As a consequence, we prove a…

Generalizing Pisier's idea, we introduce a Hilbertian matrix cross normed space associated with a pair of symmetric normed ideals. When the two ideals coincide, we show that our construction gives an operator space if and only if the ideal…

We study the approximation of operators acting on probability measures on a product space with prescribed marginal. Let $I$ be a label space endowed with a reference measure $\lambda$, and define $\cal M_\lambda$ as the set of probability…

Experimental design is an approach for selecting samples among a given set so as to obtain the best estimator for a given criterion. In the context of linear regression, several optimal designs have been derived, each associated with a…

In this paper, we compute the exact value of the norm of the Hilbert matrix operator $\mathcal{H}$ acting from the classical Bloch space $\mathcal{B}$ into the logarithmically weighted Bloch space $\mathcal{B}_{\log}$, and show that it…

The statistical leverage scores of a matrix $A$ are the squared row-norms of the matrix containing its (top) left singular vectors and the coherence is the largest leverage score. These quantities are of interest in recently-popular…

Let $({\cal X},\mu)$ be a measure space. For any measurable set $Y\subset{\cal X}$ let $1_Y : {\cal X}\to{\mathbb R}$ be the indicator of $Y$ and let $\pi_Y$ be the orthogonal projector $L^2({\cal X})\ni f\mapsto\pi_Y f = 1_Y f$. For any…

We consider (max,+)-algebra products of random matrices, which arise from performance evaluation of acyclic fork-join queueing networks. A new algebraic technique to examine properties of the product and investigate its limiting behaviour…

Let $H_1$, $H_2$ be complex Hilbert spaces. A bounded linear operator $T : H_1 \to H_2$ is said to be norm attaining if there exists a unit vector $x \in H_1$ such that $\|Tx\| = \|T\|$. If $T|_{M} : M \to H_2$ is norm attaining for every…

In this paper, we prove \( L^p \) boundedness results for lacunary elliptic maximal operators on the Heisenberg group. Furthermore, we extend these \( L^p \) estimates from skew-symmetric matrices, which naturally arise in Heisenberg group…

Fix integers $m\ge 2$, $n\ge 1$. We prove the existence of a bounded linear extension operator for $C^{m-1,1}(\R^n)$ with operator norm at most $\exp(\gamma D^k)$, where $D := \binom{m+n-1}{n}$ is the number of multiindices of length $n$…

We prove an O(log n) bound for the expected value of the logarithm of the componentwise (and, a fortiori, the mixed) condition number of a random sparse n x n matrix. As a consequence, small bounds on the average loss of accuracy for…

In this paper we prove the optimal upper bound $\frac{\lambda_{n}}{\lambda_{m}}\leq\frac{n^{2}}{m^{2}}$ $\Big(\lambda_{n}>\lambda_{m}\geq 11\sup\limits_{x\in[0,1]}q(x)\Big)$ for one-dimensional Schrodinger operators with a nonnegative…

Random matrix theory has played an important role in various areas of pure mathematics, mathematical physics, and machine learning. From a practical perspective of data science, input data are usually normalized prior to processing. Thus,…

We refine a recent result of Drury concerning the optimal ratio between the norm and numerical radius of a bounded linear operator $T$ with numerical range lying in a sector of a circular disk. In particular, characterization is given to…

For a normal measurable operator $a$ affiliated with a von Neumann factor $\mathcal{M}$ we show: If $\mathcal{M}$ is infinite, then there is $\lambda_0\in \mathbb{C}$ so that for $\varepsilon>0$ there are…