### Category: Random Matrix Theory

### Wigner and Marcenko Pastur Theorems

I. Wigner’s theorem DefinitionLet . The probability distribution on defined by is called the semi-circular distribution. We denote . Wigner’s Theorem– Let i.i.d. centered, complex valued and with . – Let i.i.d. centered, real valued with . – The ‘s and the ‘s () are independent. – Consider and the hermitian matrices defined

### Slepian and Gordon Theorems with application

In this post, we present two important results of the field of Gaussian Processes: the Slepian and Gordon Theorems. For both of them, we illustrate their power giving specific applications to random matrix theory. More precisely, we derive bounds on the expected operator norm of gaussian matrices. 1. Slepian’s Theorem and application Theorem (Slepian Fernique