Abstract
We derive a multiscale generalisation of the Bakry-Émery 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-Émery criterion, but we show that it remains effective for measures that are far from log-concave. Indeed, using our criterion, we prove that the massive continuum sine-Gordon model with β < 6π satisfies asymptotically optimal log-Sobolev inequalities for Glauber and Kawasaki dynamics. These dynamics can be seen as singular SPDEs recently constructed via regularity structures, but our results are independent of this theory.
Original language | English (US) |
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Pages (from-to) | 2064-2113 |
Number of pages | 50 |
Journal | Communications on Pure and Applied Mathematics |
Volume | 74 |
Issue number | 10 |
DOIs | |
State | Published - Oct 2021 |
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics