Poincaré inequalities and hitting times
Year: 2010
Type: preprint
Abstract: Equivalence of the spectral gap, exponential integrability of hitting times and Lyapunov conditions are well known. We give here the correspondance (with quantitative results) for reversible diffusion processes. As a consequence, we generalize results of Bobkov in the one dimensional case on the value of the Poincaré constant for logconcave measures to superlinear potentials. Finally, we study various functional inequalities under different hitting times integrability conditions (polynomial, ...). In particular, in the one dimensional case, ultracontractivity is equivalent to a bounded Lyapunov condition.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W2952185771