Some remarks on weighted logarithmic Sobolev inequality
نویسندگان
چکیده
We give here a simple proof of weighted logarithmic Sobolev inequality, for example for Cauchy type measures, with optimal weight, sharpening results of BobkovLedoux [12]. Some consequences are also discussed.
منابع مشابه
An Inequality for Relative Entropy and Logarithmic Sobolev Inequalities in Euclidean Spaces
for any density function p(x) on R, where pi(·|y1, . . . , yi−1, yi+1, . . . , yn) and Qi(·|x1, . . . , xi−1, xi+1, . . . , xn) denote the local specifications of p resp. q, and ρi is the logarithmic Sobolev constant of Qi(·|x1, . . . , xi−1, xi+1, . . . , xn). Thereby we derive a logarithmic Sobolev inequality for a weighted Gibbs sampler governed by the local specifications of q. Moreover, th...
متن کاملLogarithmic Sobolev Trace Inequality
A logarithmic Sobolev trace inequality is derived. Bounds on the best constant for this inequality from above and below are investigated using the sharp Sobolev inequality and the sharp logarithmic Sobolev inequality. Logarithmic Sobolev inequalities capture the spirit of classical Sobolev inequalities with the logarithm function replacing powers, and they can be considered as limiting cases of...
متن کاملExtremal functions for Caffarelli-Kohn-Nirenberg and logarithmic Hardy inequalities
We consider a family of Caffarelli-Kohn-Nirenberg interpolation inequalities and weighted logarithmic Hardy inequalities which have been obtained recently as a limit case of the first ones. We discuss the ranges of the parameters for which the optimal constants are achieved by extremal functions. The comparison of these optimal constants with the optimal constants of Gagliardo-Nirenberg interpo...
متن کاملLogarithmic Sobolev, Isoperimetry and Transport Inequalities on Graphs
In this paper, we study some functional inequalities (such as Poincaré inequality, logarithmic Sobolev inequality, generalized Cheeger isoperimetric inequality, transportation-information inequality and transportation-entropy inequality) for reversible nearest-neighbor Markov processes on connected finite graphs by means of (random) path method. We provide estimates of the involved constants.
متن کاملAn Explicit Bound on the Logarithmic Sobolev Constant of Weakly Dependent Random Variables
We prove logarithmic Sobolev inequality for measures q(x) = dist(X) = exp ( −V (x) ) , x ∈ R, under the assumptions that: (i) the conditional distributions Qi(·|xj , j 6= i) = dist(Xi|Xj = xj , j 6= i) satisfy a logarithmic Sobolev inequality with a common constant ρ, and (ii) they also satisfy some condition expressing that the mixed partial derivatives of the Hamiltonian V are not too large r...
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 2017