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 Anita Kollwitz
Geändert am Wednesday, 28.04.2021 14:59 von Anita Kollwitz
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