Fokker-Planck equations and one-dimensional functional inequalities for heavy tailed densities
Probability
2020-11-13 v2 Mathematical Physics
Functional Analysis
math.MP
Abstract
We study one-dimensional functional inequalities of the type of Poincar\'e, logarithmic Sobolev and Wirtinger, with weight, for probability densities with polynomial tails. As main examples, we obtain sharp inequalities satisfied by inverse Gamma densities, taking values on , and Cauchy-type densities, taking values on . In this last case, we improve the result obtained by Bobkov and Ledoux in 2009 by introducing a better weight function in the logarithmic Sobolev inequality. The results are obtained by resorting to Fokker-Planck type equations which possess these densities as steady states.
Keywords
Cite
@article{arxiv.2011.01610,
title = {Fokker-Planck equations and one-dimensional functional inequalities for heavy tailed densities},
author = {Giulia Furioli and Ada Pulvirenti and Elide Terraneo and Giuseppe Toscani},
journal= {arXiv preprint arXiv:2011.01610},
year = {2020}
}