Session S38 - Geometric Potential Analysis

Thursday, July 15, 16:40 ~ 17:10 UTC-3

Log-Sobolev inequalities and the renormalisation group

Roland Bauerschmidt

University of Cambridge, United Kingdom   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

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.)

Joint work with Thierry Bodineau (Ecole Polytechnique, France).

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