Poincaré inequalities and hitting times

Details Poincaré inequalities and hitting times Poincaré inequalities and hitting times

2010-12-23

arxiv.org/abs/1012.5274v1

Mathematics

Probability

Scientific paper

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 Poincar\'e 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.

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