A simple proof of log-Sobolev inequalities on a path space with Gibbs measures

Kawabi H

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A simple proof of log-Sobolev inequalities on a path space with Gibbs measures

机译：用吉布斯测度简单证明路径空间上的对数Sobolev不等式

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摘要

In this paper, we give a simple proof of log-Sobolev inequalities on an infinite volume path space C(R, Rd) with Gibbs measures. We introduce a parabolic stochastic partial differential equation which is reversible with respect to the Gibbs measures. In the proof, the gradient estimate for the diffusion semigroup which is derived from the stochastic flow plays a central role.

机译：在本文中，我们使用吉布斯测度给出了无限体积路径空间C（R，Rd）上log-Sobolev不等式的简单证明。我们介绍了一个抛物型随机偏微分方程，该方程相对于吉布斯测度是可逆的。在证明中，源自随机流的扩散半群的梯度估计起着中心作用。

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《Infinite dimensional analysis, quantum probability, and related topics》 |2006年第2期|共9页
作者
Kawabi H;
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正文语种 eng
中图分类物理学;
关键词
log-Sobolev inequality; Gibbs measure; SPDE; gradient estimate; FUNCTIONAL INEQUALITIES; DIFFERENTIAL-EQUATIONS; HARNACK;

机译：对数Sobolev不等式;Gibbs测度;SPDE;梯度估计;功能不等式;微分方程;危害;

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专利

1. A simple proof of log-Sobolev inequalities on a path space with Gibbs measures [J] . Kawabi H Infinite dimensional analysis, quantum probability, and related topics . 2006,第2期

机译：用吉布斯测度简单证明路径空间上的对数Sobolev不等式
2. Functional Inequalities And Uniqueness Of The Gibbs Measure- From Log-sobolev To Poincare [J] . Pierre-Andre Zitt ESAIM . 2008,第期

机译：Gibbs测度的功能不等式和唯一性-从对数sobolev到Poincare
3. Dirichlet forms and Dirichlet operators for Gibbs measures of quantum unbounded spin systems: Essential self-adjointness and log-Sobolev inequality [J] . Lim HY., Yoo HJ., Park YM. Journal of Statistical Physics . 1998,第3a4期

机译：量子无界自旋系统的吉布斯测度的Dirichlet形式和Dirichlet算符：本质自伴和对数Sobolev不等式
4. Entropy, compound Poisson approximation, log-Sobolev inequalities and measure concentration [C] . Kontoyiannis L., Madiman M. Information Theory Workshop, 2004. IEEE . 2004

机译：熵，复合泊松近似，对数Sobolev不等式和测量浓度
5. Uniqueness of Gibbs measures with application to Gibbs sampling and the Sum-Product algorithm. [D] . Winkler, Stephan Norbert. 2007

机译：Gibbs度量的唯一性及其在Gibbs采样和Sum-Product算法中的应用。
6. Cellular Telephones Measure Activity and Lifespace in Community-Dwelling Adults: Proof of Principle [O] . Ana Katrin Schenk, Bradley C. Witbrodt, Carrie A. Hoarty, -1

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7. Log-Sobolev Inequalities for Infinite dimensional Gibbs measures of higher order Interactions [O] . Papageorgiou, Ioannis 2014

机译：无穷维Gibbs测度的Log-sobolev不等式更高阶的相互作用

A simple proof of log-Sobolev inequalities on a path space with Gibbs measures

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