Generalized Γ Calculus and Application to Interacting Particles on a Graph View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-04

AUTHORS

Pierre Monmarché

ABSTRACT

The classical Bakry-Émery calculus is extended to study, for degenerated (non-elliptic, non-reversible, or non-diffusive) Markov processes, questions such as hypoellipticity, hypocoercivity, functional inequalities or Wasserstein contraction. In particular we obtain the optimal speed of convergence to equilibrium for any ergodic Ornstein-Uhlenbeck process, which is given by the spectral gap of the drift matrix and the size of the corresponding Jordan blocks. We also study chains of N interacting overdamped particles and establish for their invariant measures log-Sobolev inequalities with constants of order N2, which is optimal. More... »

PAGES

439-466

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11118-018-9689-3

DOI

http://dx.doi.org/10.1007/s11118-018-9689-3

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1101361858


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