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### 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

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.