Displaying similar documents to “Poincaré inequalities and dimension free concentration of measure”

Exponential concentration for first passage percolation through modified Poincaré inequalities

Michel Benaïm, Raphaël Rossignol (2008)

Annales de l'I.H.P. Probabilités et statistiques

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We provide a new exponential concentration inequality for first passage percolation valid for a wide class of edge times distributions. This improves and extends a result by Benjamini, Kalai and Schramm ( (2003)) which gave a variance bound for Bernoulli edge times. Our approach is based on some functional inequalities extending the work of Rossignol ( (2006)), Falik and Samorodnitsky ( (2007)).

Lipschitzian norm estimate of one-dimensional Poisson equations and applications

Hacene Djellout, Liming Wu (2011)

Annales de l'I.H.P. Probabilités et statistiques

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By direct calculus we identify explicitly the lipschitzian norm of the solution of the Poisson equation in terms of various norms of , where is a Sturm–Liouville operator or generator of a non-singular diffusion in an interval. This allows us to obtain the best constant in the 1-Poincaré inequality (a little stronger than the Cheeger isoperimetric inequality) and some sharp transportation–information inequalities and concentration inequalities for empirical means. We conclude with several...

Transportation inequalities for stochastic differential equations of pure jumps

Liming Wu (2010)

Annales de l'I.H.P. Probabilités et statistiques

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For stochastic differential equations of pure jumps, though the Poincaré inequality does not hold in general, we show that 1 transportation inequalities hold for its invariant probability measure and for its process-level law on right continuous paths space in the 1-metric or in uniform metrics, under the dissipative condition. Several applications to concentration inequalities are given.