A modified logarithmic Sobolev inequality for the Hamming cube and some applications
نویسنده
چکیده
The logarithmic Sobolev inequality [9] for the Hamming cube {0, 1} states that for any real-valued function f on the cube holds
منابع مشابه
Spectral Gap and Logarithmic Sobolev Inequality for Kawasaki and Giauber Dynamics
We prove that the spectral gap of the Kawasaki dynamics shrink at the rate of I lL 2 for cubes of size L provided that some mixing conditions are satisfied. We also prove that the logarithmic Sobolev inequality for the Glauber dynamics in standard cubes holds uniformly in the size of the cube if the Dobrushin-Shlosman mixing condition holds for standard cubes.
متن کاملFrom the Prékopa-Leindler inequality to modified logarithmic Sobolev inequality
We develop in this paper an improvement of the method given by S. Bobkov and M. Ledoux in [BL00]. Using the Prékopa-Leindler inequality, we prove a modified logarithmic Sobolev inequality adapted for all measures on Rn, with a strictly convex and super-linear potential. This inequality implies modified logarithmic Sobolev inequality, developed in [GGM05, GGM07], for all uniformly strictly conve...
متن کاملLogarithmic Sobolev inequality for log-concave measure from Prékopa-Leindler inequality
We develop in this paper an amelioration of the method given by S. Bobkov and M. Ledoux in [BL00]. We prove by Prékopa-Leindler Theorem an optimal modified logarithmic Sobolev inequality adapted for all log-concave measure on Rn. This inequality implies results proved by Bobkov and Ledoux, the Euclidean Logarithmic Sobolev inequality generalized in the last years and it also implies some convex...
متن کاملModified Logarithmic Sobolev Inequalities in Discrete Settings
Motivated by the rate at which the entropy of an ergodic Markov chain relative to its stationary distribution decays to zero, we study modified versions of logarithmic Sobolev inequalities in the discrete setting of finite Markov chains and graphs. These inequalities turn out to be weaker than the standard log-Sobolev inequality, but stronger than the Poincare’ (spectral gap) inequality. We sho...
متن کاملModified logarithmic Sobolev inequalities on R F . Barthe and
We provide a sufficient condition for a measure on the real line to satisfy a modified logarithmic Sobolev inequality, thus extending the criterion of Bobkov and Götze. Under mild assumptions the condition is also necessary. Concentration inequalities are derived. This completes the picture given in recent contributions by Gentil, Guillin and Miclo.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008