Poincaré inequalities and hitting times
By Patrick Cattiaux, Arnaud Guillin, Pierre-André Zitt. 2010
53 citations recorded by the source corpus.
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 Poincare 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.
Subfields: Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/d344218541b4e372aa42e23769d700e602a212f0
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In Mathematical Physics
- Arnaud Guillin
- Patrick Cattiaux
- Oleg Butkovsky
- Liming Wu
- Raphael Zimmer
- Andreas Eberle
- Pierre-André Zitt
- Eric Moulines
In Statistics and Probability
- Arnaud Guillin
- Patrick Cattiaux
- Andreas Eberle
- Nathael Gozlan
- Pierre-André Zitt
- Liming Wu
- Oleg Butkovsky
- Raphael Zimmer
Citations in the corpus
- Semi Log-Concave Markov Diffusions (2013, background): “12 in [20] being restricted to the variance control.”