Poincaré inequalities and hitting times

@article{Cattiaux2010PoincarIA,
  title={Poincar{\'e} inequalities and hitting times},
  author={Patrick Cattiaux and Arnaud Guillin and Pierre-Andr{\'e} Zitt},
  journal={Annales De L Institut Henri Poincare-probabilites Et Statistiques},
  year={2010},
  volume={49},
  pages={95-118}
}
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… 

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