Functional inequalities for discrete gradients and application to the geometric distribution

Joulin, Aldéric, and Privault, Nicolas. "Functional inequalities for discrete gradients and application to the geometric distribution." ESAIM: Probability and Statistics 8 (2010): 87-101. <http://eudml.org/doc/104325>.

@article{Joulin2010,
abstract = { We present several functional inequalities for finite difference gradients, such as a Cheeger inequality, Poincaré and (modified) logarithmic Sobolev inequalities, associated deviation estimates, and an exponential integrability property. In the particular case of the geometric distribution on $\{\mathbb\{N\}\}$ we use an integration by parts formula to compute the optimal isoperimetric and Poincaré constants, and to obtain an improvement of our general logarithmic Sobolev inequality. By a limiting procedure we recover the corresponding inequalities for the exponential distribution. These results have applications to interacting spin systems under a geometric reference measure. },
author = {Joulin, Aldéric, Privault, Nicolas},
journal = {ESAIM: Probability and Statistics},
keywords = {Geometric distribution; isoperimetry; logarithmic Sobolev inequalities; spectral gap; Herbst method; deviation inequalities; Gibbs measures. ; logarithmic Sobolev inequalities; deviation inequalities; Gibbs measures},
language = {eng},
month = {3},
pages = {87-101},
publisher = {EDP Sciences},
title = {Functional inequalities for discrete gradients and application to the geometric distribution},
url = {http://eudml.org/doc/104325},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Joulin, Aldéric
AU - Privault, Nicolas
TI - Functional inequalities for discrete gradients and application to the geometric distribution
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 8
SP - 87
EP - 101
AB - We present several functional inequalities for finite difference gradients, such as a Cheeger inequality, Poincaré and (modified) logarithmic Sobolev inequalities, associated deviation estimates, and an exponential integrability property. In the particular case of the geometric distribution on ${\mathbb{N}}$ we use an integration by parts formula to compute the optimal isoperimetric and Poincaré constants, and to obtain an improvement of our general logarithmic Sobolev inequality. By a limiting procedure we recover the corresponding inequalities for the exponential distribution. These results have applications to interacting spin systems under a geometric reference measure.
LA - eng
KW - Geometric distribution; isoperimetry; logarithmic Sobolev inequalities; spectral gap; Herbst method; deviation inequalities; Gibbs measures. ; logarithmic Sobolev inequalities; deviation inequalities; Gibbs measures
UR - http://eudml.org/doc/104325
ER -