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10 - Optimal coupling for mean field limits

from PART 2 - SURVEYS AND RESEARCH PAPERS

Published online by Cambridge University Press:  05 August 2014

François Bolley
Affiliation:
Université de Paris IX
Yann Ollivier
Affiliation:
Université de Paris XI
Hervé Pajot
Affiliation:
Université de Grenoble
Cedric Villani
Affiliation:
Université de Paris VI (Pierre et Marie Curie)
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Summary

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Type
Chapter
Information
Optimal Transport
Theory and Applications
, pp. 266 - 273
Publisher: Cambridge University Press
Print publication year: 2014

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References

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[2] D., Benedetto, E., Caglioti, J.A., Carrillo and M., Pulvirenti. A non-Maxwellian steady distribution for one-dimensional granular media. J. Statist. Phys. 91, 5-6 (1998), 979–990.Google Scholar
[3] F., Bolley, J.A., Cañizo and J.A., Carrillo. Stochastic mean-field limit: non-Lipschitz forces and swarming. Math. Mod. Meth. Appi. Sci. 21, 11 (2011), 2179–2210.Google Scholar
[4] F., Bolley, A., Guillin and F., Malrieu. Trend to equilibrium and particle approximation for a weakly selfconsistent Vlasov-Fokker-Planck equation. Math. Mod. Num. Anal. 44, 5 (2010) 867–884.Google Scholar
[5] F., Bolley, A., Guillin and C., Villani. Quantitative concentration inequalities for empirical measures on non-compact spaces. Prob. Theor. Rel. Fields 137, 3-1 (2007), 541–593.Google Scholar
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[7] P., Cattiaux, A., Guillin and F., Malrieu. Probabilistic approach for granular media equations in the non uniformly case. Prob. Theor. Rel. Fields 140, 1-2 (2008), 19–40.Google Scholar
[8] J., Dolbeault. Free energy and solutions of the Vlasov-Poisson-Fokker-Planck system: external potential and confinement (large time behavior and steady states). J. Math. Pures Appl. 9, 78, 2 (1999), 121–157.Google Scholar
[9] F., Malrieu. Logarithmic Sobolev inequalities for some nonlinear PDE's. Stoch. Proc. Appl. 95, 1 (2001), 109–132.Google Scholar
[10] F., Malrieu. Convergence to equilibrium for granular media equations and their Euler schemes. Ann. Appl. Probab. 13, 2 (2003), 540–560.Google Scholar
[11] S., Meleard. Asymptotic Behaviour of Some Interacting Particle Systems; McKean-Vlasov and Boltzmann models. Lecture Notes in Mathematics 1627, Springer, Berlin, 1996.
[12] A.-S., Sznitman. Topics in Propagation of Chaos. Lecture Notes in Mathematics 1464, Springer, Berlin, 1991.
[13] C., Villani. Optimal Transport, Old and New. Grundlehren der mathematischen Wissenschaften 338, Springer, Berlin, 2009.

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