Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-08T07:19:45.795Z Has data issue: false hasContentIssue false

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)
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Optimal Transport
Theory and Applications
, pp. 266 - 273
Publisher: Cambridge University Press
Print publication year: 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] S., Benachour, B., Roynette, D., Talay and P., Vallois. Nonlinear self-stabilizing processes. I. Existence, invariant probability, propagation of chaos. Stoch. Proc. Appl. 75, 2(1998), 173–201.Google Scholar
[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
[6] J.A., Carrillo, R.J., McCann and C., Villani. Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates. Rev. Mat. Iberoamericana 19, 3 (2003), 971–1018.Google Scholar
[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.

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×