Log‐Sobolev Inequality for the Continuum Sine‐Gordon Model
Authors
Bauerschmidt, Roland
Bodineau, Thierry
Publication Date
2020-07-11Journal Title
Communications on Pure and Applied Mathematics
ISSN
0010-3640
1097-0312
Publisher
John Wiley & Sons Australia, Ltd
Volume
74
Issue
10
Pages
2064-2113
Language
en
Type
Article
This Version
AO
VoR
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Bauerschmidt, R., & Bodineau, T. (2020). Log‐Sobolev Inequality for the Continuum Sine‐Gordon Model. Communications on Pure and Applied Mathematics, 74 (10), 2064-2113. https://doi.org/10.1002/cpa.21926
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. © 2021 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.
Keywords
Research Article, Research Articles
Identifiers
cpa21926
External DOI: https://doi.org/10.1002/cpa.21926
This record's URL: https://www.repository.cam.ac.uk/handle/1810/326811
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Licence:
http://creativecommons.org/licenses/by-nc-nd/4.0/
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