Stochastic dynamics and the Polchinski equation: an introduction
Abstract
This introduction surveys a renormalisation group perspective on logSobolev 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 Föllmer process, the BouéDupuis variational formula and the BarashkovGubinelli approach, the transportation of measure perspective, and the classical analogues of these ideas for HamiltonJacobi equations which arise in meanfield limits.
 Publication:

arXiv eprints
 Pub Date:
 July 2023
 DOI:
 10.48550/arXiv.2307.07619
 arXiv:
 arXiv:2307.07619
 Bibcode:
 2023arXiv230707619B
 Keywords:

 Mathematics  Probability;
 Mathematical Physics;
 Mathematics  Functional Analysis