Holger Sambale (Bielefeld): Higher Order Concentration of Measure via Log-Sobolev Inequalities(Oberseminar Mathematische Stochastik)

Wednesday, 05.05.2021 17:00 per ZOOM: 61828242813

Mathematik und Informatik

We investigate higher order versions of the concentration of measure phenomenon by means of logarithmic Sobolev inequalities. The functions we consider are non-Lipschitz but have bounded derivatives (or differences) of some higher order $d$. This results in exponential tail bounds which are no longer sub-Gaussian but, for large $t$, typically decay like $\exp(-t^{2/d})$. Our main tool is the entropy method, more precisely $L^p$ norm inequalities derived from log-Sobolev inequalities. A special focus is put on so-called finite spin systems, or functions of weakly dependent random variables, for which we derive log-Sobolev inequalities under suitable (Dobrushin-type) conditions. This is joint work with S. Bobkov, F. Götze and A. Sinulis.

Angelegt am Thursday, 25.03.2021 11:35 von kollwit
Geändert am Wednesday, 28.04.2021 14:59 von kollwit
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