Talagrand's inequality for Interacting Particle Systems satisfying a log-Sobolev inequality

Florian Völlering

Talagrand's inequality for Interacting Particle Systems satisfying a log-Sobolev inequality

Probability 2014-05-23 v2

Authors: Florian Völlering

Abstract

Talagrand's inequality for independent Bernoulli random variables is extended to many interacting particle systems (IPS). The main assumption is that the IPS satisfies a log-Sobolev inequality. In this context it is also shown that a slightly stronger version of Talagrand's inequality is equivalent to a log-Sobolev inequality. Additionally we also look at a common application, the relation between the probability of increasing events and the influences on that event by changing a single spin.

Keywords

Talagrand's inequality interacting particle systems log-Sobolev inequality Bernoulli random variables increasing events influences

Cite

@article{arxiv.1306.2868,
  title  = {Talagrand's inequality for Interacting Particle Systems satisfying a log-Sobolev inequality},
  author = {Florian Völlering},
  journal= {arXiv preprint arXiv:1306.2868},
  year   = {2014}
}

Comments

Russo's formula and related estimates added; mistake in proof fixed; restructured for easier reading

Talagrand's inequality for Interacting Particle Systems satisfying a log-Sobolev inequality

Abstract

Keywords

Cite

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