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.

arXiv commentAccepted version, to appear in CPAM

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Cited by in corpus (13)

• Renormalization Group Flow as Optimal Transport
• Log-Sobolev inequality for near critical Ising models
• Maximum and coupling of the sine-Gordon field
• A stochastic analysis approach to lattice Yang--Mills at strong coupling
• The Coleman correspondence at the free fermion point
• Flow equation approach to singular stochastic PDEs
• Stochastic dynamics and the Polchinski equation: an introduction
• 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
• Conservative stochastic 2-dimensional Cahn-Hilliard equation
• 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