The free logarithmic Sobolev and the free transportation cost inequalities by time integrations

被引：1

作者：

Nemoto, Aya ^{[1
]}

Yoshida, Hiroaki ^{[2
]}

机构：

[1] Ochanomizu Univ, Dept Math, Bunkyo Ku, Tokyo 1128610, Japan

[2] Ochanomizu Univ, Dept Informat Sci, Bunkyo Ku, Tokyo 1128610, Japan

来源：

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS | 2014年 / 17卷 / 03期

关键词：

Relative free entropy; relative free Fisher information; free functional inequalities; FREE ENTROPY; EQUATIONS; OPERATORS;

D O I：

10.1142/S0219025714500222

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we shall revisit the free analogues of the logarithmic Sobolev and the transportation cost inequalities for one-dimensional case by time integrations. We consider time evolutions by the free Fokker-Planck equation and calculate the time derivative of the 2-Wasserstein distance with the optimal mass transportation, from which some differential inequalities can be derived. The convergence to the equilibrium in the relative free entropy is discussed, and the free transportation cost and the free logarithmic Sobolev inequalities can be obtained by time integrations.

引用

页数：24

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