Roland Bauerschmidt (Cambridge)

Log-Sobolev inequality for the continuum Sine-Gordon model

Abstract:
We derive a multiscale generalisation of the Bakry--Emery 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--Emery criterion, but we show that it remains effective for measures which are far from log-concave. Indeed, as an application, we prove that the massive continuum Sine-Gordon model with \beta < 6\pi satisfies asymptotically optimal Log-Sobolev inequalities for Glauber and Kawasaki dynamics. (This is joint work with Thierry Bodineau.)