Volume 8, August 2004
|Page(s)||87 - 101|
|Published online||15 September 2004|
Functional inequalities for discrete gradients and application to the geometric distribution
Laboratoire de Mathématiques, Université de La Rochelle, avenue Michel Crépeau,
17042 La Rochelle Cedex, France; firstname.lastname@example.org.; email@example.com.
Revised: 3 February 2004
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 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.
Mathematics Subject Classification: 60E07 / 60E15 / 60K35
Key words: Geometric distribution / isoperimetry / logarithmic Sobolev inequalities / spectral gap / Herbst method / deviation inequalities / Gibbs measures.
© EDP Sciences, SMAI, 2004
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.