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Stochastic dynamics and the Polchinski equation: an introduction
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This introduction surveys a renormalisation group perspective on log-Sobolev inequalities and related properties of stochastic dynamics. We also explain the relationship of this approach to related recent and less recent developments such as Eldan's stochastic localisation and the F\"ollmer process, the Bou\'e--Dupuis variational formula and the Barashkov--Gubinelli approach, the transportation of measure perspective, and the classical analogues of these ideas for Hamilton--Jacobi equations which arise in mean-field limits.
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Cited by 2 Pith papers
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On free energy of non-convex multi-species spin glasses
The free energy limit of a non-convex multi-species spin glass, if it exists, is a critical value of the Hamilton-Jacobi functional.
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Lecture notes on the flow equation approach to singular stochastic PDEs
A scale-by-scale flow equation with suitably chosen counterterms constructs renormalized solutions of fractional elliptic Phi^4 SPDEs throughout the subcritical regime.
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