Measure concentration through non-Lipschitz observables and functional inequalities

Arnaud Guillin; Aldéric Joulin

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arXiv · 1202.2341

Measure concentration through non-Lipschitz observables and functional inequalities

Arnaud Guillin·Aldéric Joulin

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Abstract

Non-Gaussian concentration estimates are obtained for invariant probability measures of reversible Markov processes. We show that the functional inequalities approach combined with a suitable Lyapunov condition allows us to circumvent the classical Lipschitz assumption of the observables. Our method is general and covers diffusions as well as pure-jump Markov processes on unbounded spaces.

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Arnaud Guillin, Aldéric Joulin. 2012-02-10. Measure concentration through non-Lipschitz observables and functional inequalities. https://arxiv.org/abs/1202.2341

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