Workshop MESA - Stein's Method and Applications

Total variation bound for Hadwiger's functional using Stein's method

22 mars 2023, 10:25

55m

Amphi Schwartz (Institut de Mathématiques de Toulouse)

Orateur

Ivan Nourdin (University of Luxembourg)

Description

Let $K$ be a convex body in ${\mathbb{R}}^d$. Let $X_K$ be a $d$-dimensional random vector distributed according to the Hadwiger-Wills density ${\mu }_K$ associated with $K$, defined as ${\mu }_K(x)=c{e}^{-\pi {\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{t}}^2(x,K)}$, $x\in {\mathbb{R}}^d$. Finally, let the information content $H_K$ be defined as $H_K={\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{t}}^2(X_K,K)$.

In this talk, we will study the fluctuations of $H_K$ around its expectation as the dimension $d$ go to infinity.
Stein's method plays a crucial role in our analysis.
This is joint work with Valentin Garino.

Documents de présentation

Exposé Toulouse-Ivan Nourdin.pdf