Log-Sobolev inequality for the continuum sine-Gordon model

We derive a multiscale generalisation of the Bakry-Emery criterion for a measure to satisfy a Log-Sobolev inequality. Our criterion relies on the Polchinski equation which is well known in renormalisation theory. This multiscale approach implies the usual Bakry-Emery criterion, but we show that it remains effective for measures which are far from log-concave. In particular, it applies to the Glauber and Kawasaki dynamics of the massive continuum sine-Gordon model with $\beta < 6 \pi$ and leads to asymptotically optimal Log-Sobolev inequalities.

This is joint work with Roland Bauerschmidt.