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

Florian Völlering

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arXiv · 1306.2868

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

Florian Völlering

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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.

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Florian Völlering. 2014-05-22. Talagrand's inequality for Interacting Particle Systems satisfying a log-Sobolev inequality. https://arxiv.org/abs/1306.2868

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