Log-Sobolev inequality for the continuum sine-Gordon model

Abstract

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 which are far from log-concave. Indeed, using our criterion, we prove that the massive continuum Sine-Gordon model with $\beta <6\pi$ 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.

Accepted version, to appear in CPAM

References in corpus (2)

• Introduction to a renormalisation group method
• A probabilistic approach of ultraviolet renormalisation in the boundary Sine-Gordon model

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• Log-Sobolev inequality for the ${\phi }_2^4$ and ${\phi }_3^4$ measures
• Kawasaki dynamics beyond the uniqueness threshold
• Spectral gap in mean-field $\mathcal{O}(n)$-model
• Local operators in the Sine-Gordon model: ${\partial }_{\mu }\varphi {\partial }_{\nu }\varphi$ and the stress tensor
• Multiscale coupling and the maximum of $\mathcal{P}(\varphi {)}_2$ models on the torus