Poincaré inequalities and hitting times

Patrick Cattiaux; Arnaud Guillin; Pierre André Zitt

Annales de l'I.H.P. Probabilités et statistiques (2013)

  • Volume: 49, Issue: 1, page 95-118
  • ISSN: 0246-0203

Abstract

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Equivalence of the spectral gap, exponential integrability of hitting times and Lyapunov conditions is well known. We give here the correspondence (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 log-concave 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.

How to cite

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Cattiaux, Patrick, Guillin, Arnaud, and Zitt, Pierre André. "Poincaré inequalities and hitting times." Annales de l'I.H.P. Probabilités et statistiques 49.1 (2013): 95-118. <http://eudml.org/doc/272061>.

@article{Cattiaux2013,
abstract = {Equivalence of the spectral gap, exponential integrability of hitting times and Lyapunov conditions is well known. We give here the correspondence (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 log-concave 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.},
author = {Cattiaux, Patrick, Guillin, Arnaud, Zitt, Pierre André},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {poincaré inequalities; Lyapunov functions; hitting times; log-concave measures; Poincaré–Sobolev inequalities; Poincaré inequalities; Poincaré-Sobolev inequalities},
language = {eng},
number = {1},
pages = {95-118},
publisher = {Gauthier-Villars},
title = {Poincaré inequalities and hitting times},
url = {http://eudml.org/doc/272061},
volume = {49},
year = {2013},
}

TY - JOUR
AU - Cattiaux, Patrick
AU - Guillin, Arnaud
AU - Zitt, Pierre André
TI - Poincaré inequalities and hitting times
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2013
PB - Gauthier-Villars
VL - 49
IS - 1
SP - 95
EP - 118
AB - Equivalence of the spectral gap, exponential integrability of hitting times and Lyapunov conditions is well known. We give here the correspondence (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 log-concave 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.
LA - eng
KW - poincaré inequalities; Lyapunov functions; hitting times; log-concave measures; Poincaré–Sobolev inequalities; Poincaré inequalities; Poincaré-Sobolev inequalities
UR - http://eudml.org/doc/272061
ER -

References

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