Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces

Erbar M, Fathi M, Schlichting A (2020)
ALEA: Latin American Journal of Probability and Mathematical Statistics 17(1): 445-471.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Erbar, MatthiasUniBi; Fathi, Max; Schlichting, Andre
Abstract / Bemerkung
We consider non-linear evolution equations arising from mean-field limits of particle systems on discrete spaces. We investigate a notion of curvature bounds for these dynamics based on the convexity of the free energy along interpolations in a discrete transportation distance related to the gradient flow structure of the dynamics. This notion extends the one for linear Markov chain dynamics studied in Erbar and Maas (2012). We show that positive curvature bounds entail several functional inequalities controlling the convergence to equilibrium of the dynamics. We establish explicit curvature bounds for several examples of mean-field limits of various classical models from statistical mechanics.
Stichworte
Random dynamics; random environments; K process; scaling limit; trap; models
Erscheinungsjahr
2020
Zeitschriftentitel
ALEA: Latin American Journal of Probability and Mathematical Statistics
Band
17
Ausgabe
1
Seite(n)
445-471
ISSN
1980-0436
Page URI
https://pub.uni-bielefeld.de/record/2946140

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Erbar M, Fathi M, Schlichting A. Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces. ALEA: Latin American Journal of Probability and Mathematical Statistics . 2020;17(1):445-471.
Erbar, M., Fathi, M., & Schlichting, A. (2020). Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces. ALEA: Latin American Journal of Probability and Mathematical Statistics , 17(1), 445-471. doi:10.30757/ALEA.v17-18
Erbar, M., Fathi, M., and Schlichting, A. (2020). Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces. ALEA: Latin American Journal of Probability and Mathematical Statistics 17, 445-471.
Erbar, M., Fathi, M., & Schlichting, A., 2020. Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces. ALEA: Latin American Journal of Probability and Mathematical Statistics , 17(1), p 445-471.
M. Erbar, M. Fathi, and A. Schlichting, “Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces”, ALEA: Latin American Journal of Probability and Mathematical Statistics , vol. 17, 2020, pp. 445-471.
Erbar, M., Fathi, M., Schlichting, A.: Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces. ALEA: Latin American Journal of Probability and Mathematical Statistics . 17, 445-471 (2020).
Erbar, Matthias, Fathi, Max, and Schlichting, Andre. “Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces”. ALEA: Latin American Journal of Probability and Mathematical Statistics 17.1 (2020): 445-471.

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