Zusammenfassung für den Vortrag am 17.09.2020 (17:00 Uhr)Webinar “Analysis, Quantum Fields, and Probability”
Thierry Bodineau (École Polytechnique)
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.
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