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Log-Sobolev inequality for the continuum Sine-Gordon model

Banff International Research Station for Mathematical Innovation and Discovery

I will present a multiscale generalisation of the Bakry--Emery criterion for a measure to satisfy a Log-Sobolev inequality. It 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, we prove that the massive continuum Sine-Gordon model on $R^2$ with $\beta < 6\pi$ 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. This is joint work with T. Bodineau.

Mathematics; Probability theory and stochastic processes; Mechanics of particles and systems

video/mp4

Author affiliation: Cambridge University

2020-02-05

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/73477

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/