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.)