Log-Sobolev Inequality for the Continuum Sine-Gordon Model - ANR - Agence nationale de la recherche
Article Dans Une Revue Commun.Pure Appl.Math. Année : 2021

Log-Sobolev Inequality for the Continuum Sine-Gordon Model

Résumé

We derive a multiscale generalisation of the Bakry-Émery criterion for a measure to satisfy a log-Sobolev inequality. Our criterion relies on the control of an associated PDE well-known in renormalisation theory: the Polchinski equation. It implies the usual Bakry-Émery criterion, but we show that it remains effective for measures that are far from log-concave. Indeed, using our criterion, we prove that the massive continuum sine-Gordon model with β < 6π satisfies asymptotically optimal log-Sobolev inequalities for Glauber and Kawasaki dynamics. These dynamics can be seen as singular SPDEs recently constructed via regularity structures, but our results are independent of this theory. © 2021 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.

Dates et versions

hal-02283543 , version 1 (10-09-2019)

Identifiants

Citer

Roland Bauerschmidt, Thierry Bodineau. Log-Sobolev Inequality for the Continuum Sine-Gordon Model. Commun.Pure Appl.Math., 2021, 74 (10), pp.2064-2113. ⟨10.1002/cpa.21926⟩. ⟨hal-02283543⟩
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