## View abstract

### Session S17 - Stochastic Systems: Analysis, Numerics and Applications

Tuesday, July 13, 11:00 ~ 11:35 UTC-3

## Titre: Behavior of the Wishart rsndom matrix with entries in Wiener chaos

### Ciprian Tudor

#### University of Lille, France   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak0ce203ff8ce7c83ebc1220e1d1ec0456').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy0ce203ff8ce7c83ebc1220e1d1ec0456 = 'c&#105;pr&#105;&#97;n.t&#117;d&#111;r' + '&#64;'; addy0ce203ff8ce7c83ebc1220e1d1ec0456 = addy0ce203ff8ce7c83ebc1220e1d1ec0456 + '&#117;n&#105;v-l&#105;ll&#101;' + '&#46;' + 'fr'; var addy_text0ce203ff8ce7c83ebc1220e1d1ec0456 = 'c&#105;pr&#105;&#97;n.t&#117;d&#111;r' + '&#64;' + '&#117;n&#105;v-l&#105;ll&#101;' + '&#46;' + 'fr';document.getElementById('cloak0ce203ff8ce7c83ebc1220e1d1ec0456').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy0ce203ff8ce7c83ebc1220e1d1ec0456 + '\'>'+addy_text0ce203ff8ce7c83ebc1220e1d1ec0456+'<\/a>';

For any $n\times d$ random matrix $X$, one can associate its Wishart matrix $W= X^{T}X$. The Wishart matrices are random matrices with many applications in various area. Their asymptotic behavior, when the dimensions $n$ and $d$ are large, is of great interest. We consider a random matrix $X$ whose entries are elements in a Wiener chaos of fixed order. These random entries are either independent or with a particular correlation structure, related to the correlation of the increments of a Hermite process. We discuss the limit behavior in distribution, under the Wasserstein distance, of its associated Wishart matrix. We use the Stein- Malliavin calculus and the characterisation of the independence on Wiener space. We also tackle the situation when the elements of the initial matrix $X$ are in an infinite sum of Wiener chaoses.