## View abstract

### 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. document.getElementById('cloak477045da66a6ba29a638fe74c7c1fd09').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy477045da66a6ba29a638fe74c7c1fd09 = 'rb812' + '&#64;'; addy477045da66a6ba29a638fe74c7c1fd09 = addy477045da66a6ba29a638fe74c7c1fd09 + 'c&#97;m' + '&#46;' + '&#97;c' + '&#46;' + '&#117;k'; var addy_text477045da66a6ba29a638fe74c7c1fd09 = 'rb812' + '&#64;' + 'c&#97;m' + '&#46;' + '&#97;c' + '&#46;' + '&#117;k';document.getElementById('cloak477045da66a6ba29a638fe74c7c1fd09').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy477045da66a6ba29a638fe74c7c1fd09 + '\'>'+addy_text477045da66a6ba29a638fe74c7c1fd09+'<\/a>';

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).