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Spectral gap estimates for interacting particle systems via a Bochner-type identity

Anne-Severine Boudou·Pietro Caputo·Paolo Dai Pra·Gustavo Posta
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Abstract

We develop a general technique, based on a Bochner-type identity, to estimate spectral gaps of a class of Markov operator. We apply this technique to various interacting particle systems. In particular, we give a simple and short proof of the diffusive scaling of the spectral gap of the Kawasaki model at high temperature. Similar results are derived for Kawasaki-type dynamics in the lattice without exclusion, and in the continuum. New estimates for Glauber-type dynamics are also obtained.

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Anne-Severine Boudou, Pietro Caputo, Paolo Dai Pra, Gustavo Posta. 2005-11-02. Spectral gap estimates for interacting particle systems via a Bochner-type identity. https://arxiv.org/abs/math/0505533

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