We show how to extend several basic concentration inequalities for simple random tensors
X=x_1⊗⋯⊗x_d where all x_k are independent random vectors in R^n with independent …

Let A=(a ij) be an n× n random matrix with iid entries such that E a 11= 0 and E a 11 2= 1.
We prove that for any δ> 0 there is L> 0 depending only on δ, and a subset N of B 2 n of …

A simple way to generate a Boolean function is to take the sign of a real polynomial in n
variables. Such Boolean functions are called polynomial threshold functions. How many low …

The celebrated elliptic law describes the distribution of eigenvalues of random matrices with
correlations between off-diagonal pairs of elements, having applications to a wide range of …

The empirical eigenvalue distribution of the elliptic random matrix ensemble tends to the
uniform measure on an ellipse in the complex plane as its dimension tends to infinity. We …

This is an introductory book on Non-Commutative Probability or Free Probability and Large
Dimensional Random Matrices. Basic concepts of free probability are introduced by analogy …

We investigate the joint convergence of independent random Toeplitz matrices with complex
input entries that have a pair-correlation structure, along with deterministic Toeplitz matrices …

We show that independent elliptic matrices converge to freely independent elliptic elements.
Moreover, the elliptic matrices are asymptotically free with deterministic matrices under …

We consider products of independent n× n non-Hermitian random matrices X (1),…, X (m).
Assume that their entries, X jk (q), 1≤ j, k≤ n, q= 1,…, m, are independent identically …

In the first part of this thesis, we give the theoretical foundations of random matrix theory
through the definitions of a random matrix, a random probability measure and the …