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

Aya Nemoto; Hiroaki Yoshida

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

机译：按时间积分的免费对数Sobolev和免费运输成本不平等

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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.

机译：在本文中，我们将通过时间积分重新研究对数Sobolev的自由类似物和一维情况下的运输成本不等式。我们通过自由的Fokker-Planck方程考虑时间演化，并计算具有最佳质量输运的2-Wasserstein距离的时间导数，由此可以导出一些微分不等式。讨论了相对自由熵在平衡上的收敛性，可以通过时间积分获得自由运输成本和自由对数索伯列夫不等式。

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《Infinite dimensional analysis, quantum probability, and related topics》 |2014年第3期|共24页
作者
Aya Nemoto; Hiroaki Yoshida;
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正文语种 eng
中图分类物理学;
关键词
Relative free entropy; relative free Fisher information; free functional inequalities;

机译：相对自由熵;相对自由Fisher信息;自由泛函不等式;

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1. The free logarithmic Sobolev and the free transportation cost inequalities by time integrations [J] . Aya Nemoto, Hiroaki Yoshida Infinite dimensional analysis, quantum probability, and related topics . 2014,第3期

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

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