Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces
Erbar M, Fathi M, Schlichting A (2020)
ALEA Lat. Am. J. Probab. Math. Stat. 17(1): 445-471.
Zeitschriftenaufsatz | Englisch
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Autor*in
Erbar, MatthiasUniBi;
Fathi, Max;
Schlichting, Andre
Einrichtung
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 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 by Erbar and Maas. 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.
Erscheinungsjahr
2020
Zeitschriftentitel
ALEA Lat. Am. J. Probab. Math. Stat.
Band
17
Ausgabe
1
Seite(n)
445-471
ISSN
1980-0436
Page URI
https://pub.uni-bielefeld.de/record/2980838
Zitieren
Erbar M, Fathi M, Schlichting A. Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces. ALEA Lat. Am. J. Probab. Math. Stat. 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 Lat. Am. J. Probab. Math. Stat., 17(1), 445-471. https://doi.org/10.30757/alea.v17-18
Erbar, Matthias, Fathi, Max, and Schlichting, Andre. 2020. “Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces”. ALEA Lat. Am. J. Probab. Math. Stat. 17 (1): 445-471.
Erbar, M., Fathi, M., and Schlichting, A. (2020). Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces. ALEA Lat. Am. J. Probab. Math. Stat. 17, 445-471.
Erbar, M., Fathi, M., & Schlichting, A., 2020. Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces. ALEA Lat. Am. J. Probab. Math. Stat., 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 Lat. Am. J. Probab. Math. Stat., 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 Lat. Am. J. Probab. Math. Stat. 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 Lat. Am. J. Probab. Math. Stat. 17.1 (2020): 445-471.
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