Limite de champ moyen de systèmes de particules
- [1] Ceremade, Umr Cnrs 7534 Université Paris-Dauphine Place du Maréchal de Lattre de Tassigny F-75775 Paris cedex 16
Séminaire Équations aux dérivées partielles (2009-2010)
- page 1-15
Access Full Article
topAbstract
topHow to cite
topBolley, François. "Limite de champ moyen de systèmes de particules." Séminaire Équations aux dérivées partielles (2009-2010): 1-15. <http://eudml.org/doc/251186>.
@article{Bolley2009-2010,
abstract = {On présente des résultats classiques et récents dans l’étude de la limite de champ moyen de systèmes de particules stochastiques en interaction. Ces derniers résultats visent à couvrir une plus grande variété de modèles et obtenir des estimations précises de la convergence et sont mises en lien avec le comportement en temps grand des systèmes considérés.},
affiliation = {Ceremade, Umr Cnrs 7534 Université Paris-Dauphine Place du Maréchal de Lattre de Tassigny F-75775 Paris cedex 16},
author = {Bolley, François},
journal = {Séminaire Équations aux dérivées partielles},
language = {fre},
pages = {1-15},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Limite de champ moyen de systèmes de particules},
url = {http://eudml.org/doc/251186},
year = {2009-2010},
}
TY - JOUR
AU - Bolley, François
TI - Limite de champ moyen de systèmes de particules
JO - Séminaire Équations aux dérivées partielles
PY - 2009-2010
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
SP - 1
EP - 15
AB - On présente des résultats classiques et récents dans l’étude de la limite de champ moyen de systèmes de particules stochastiques en interaction. Ces derniers résultats visent à couvrir une plus grande variété de modèles et obtenir des estimations précises de la convergence et sont mises en lien avec le comportement en temps grand des systèmes considérés.
LA - fre
UR - http://eudml.org/doc/251186
ER -
References
top- M. Agueh, R. Illner et A. Richardson. Analysis and simulations of a refined flocking and swarming model of Cucker-Smale type. Kinetic Rel. Models 4, 1 (2011), 1–16. Zbl1208.92096MR2765734
- S. Benachour, B. Roynette, D. Talay et P. Vallois. Nonlinear self-stabilizing processes. I. Existence, invariant probability, propagation of chaos. Stoch. Proc. Appl. 75, 2 (1998), 173–201. Zbl0932.60063MR1632193
- D. Benedetto, E. Caglioti, J. A. Carrillo et M. Pulvirenti. A non-Maxwellian steady distribution for one-dimensional granular media. J. Statist. Phys. 91, 5-6 (1998), 979–990. Zbl0921.60057MR1637274
- F. Bolley. Quantitative concentration inequalities on sample path space for mean field interaction. Esaim Prob. Stat. 14 (2010), 192–209. Zbl1208.82038MR2741965
- F. Bolley, J. A. Cañizo et J. A. Carrillo. Stochastic Mean-Field Limit : Non-Lipschitz Forces and Swarming. A paraître dans Math. Mod. Meth. Appl. Sci. (2011). Zbl1273.82041MR2860672
- F. Bolley, J. A. Cañizo et J. A. Carrillo. Mean-field limit for the stochastic Vicsek model. Prépublication (2011). Zbl1239.91127MR2855983
- F. Bolley, A. Guillin et 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. Zbl1201.82029MR2731396
- F. Bolley, A. Guillin et C. Villani. Quantitative concentration inequalities for empirical measures on non-compact spaces. Prob. Theor. Rel. Fields 137, 3-4 (2007), 541–593. Zbl1113.60093MR2280433
- W. Braun et K. Hepp. The Vlasov Dynamics and Its Fluctuations in the 1/N Limit of Interacting Classical Particles. Commun. Math. Phys. 56 (1977), 101–113. Zbl1155.81383MR475547
- J. A. Cañizo, J. A. Carrillo et J. Rosado. A well-posedness theory in measures for some kinetic models of collective motion. Math. Mod. Meth. Appl. Sci. 21 (2011), 515–539. Zbl1218.35005MR2782723
- E. A. Carlen, M. C. Carvalho, M. Loss, J. Le Roux et C. Villani. Entropy and chaos in the Kac model. Kinetic Rel. Models 3, 1 (2010), 85–122. Zbl1186.76675MR2580955
- J. A. Carrillo, M. Fornasier, G. Toscani et F. Vecil. Particle, Kinetic, and Hydrodynamic Models of Swarming. In Naldi, G., Pareschi, L., Toscani, G. (eds.) Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences, Series : Modelling and Simulation in Science and Technology, Birkhauser, (2010), 297–336. Zbl1211.91213MR2744704
- J. A. Carrillo, R. J. McCann et C. Villani. Kinetic equilibration rates for granular media and related equations : entropy dissipation and mass transportation estimates. Rev. Mat. Ibero. 19, 3 (2003), 971–1018. Zbl1073.35127MR2053570
- P. Cattiaux, A. Guillin et F. Malrieu. Probabilistic approach for granular media equations in the non uniformly case. Prob. Theor. Rel. Fields 140, 1-2 (2008), 19–40. Zbl1169.35031MR2357669
- F. Cucker et S. Smale. Emergent behavior in flocks. IEEE Trans. Automat. Control 52 (2007), 852–862. MR2324245
- R. Dobrushin. Vlasov equations. Funct. Anal. Appl.13 (1979), 115–123. Zbl0422.35068MR541637
- M. R. D’Orsogna, Y. L. Chuang, A. L. Bertozzi et L. Chayes. Self-propelled particles with soft-core interactions : patterns, stability, and collapse. Phys. Rev. Lett. 96, 2006.
- F. Golse The mean-field limit for the dynamics of large particle systems, Journées équations aux dérivées partielles, Forges-les-Eaux (2003), 1–47. Zbl1211.82037MR2050595
- F. Golse. The mean-field limit for a regularized Vlasov-Maxwell dynamics. Prépublication (2010). Zbl1251.82037
- M. Hauray et P.-E. Jabin. N particles approximation of the Vlasov equations with singular potential. Arch. Rach. Mech. Anal. 183, 3 (2007), 489–524. Zbl1107.76066MR2278413
- G. Loeper. Uniqueness of the solution to the Vlasov-Poisson system with bounded density. J. Math. Pures Appl. 9, 86 (2006), 68–79. Zbl1111.35045MR2246357
- F. Malrieu. Logarithmic Sobolev inequalities for some nonlinear PDE’s. Stoch. Proc. Appl. 95, 1 (2001), 109–132. Zbl1059.60084MR1847094
- F. Malrieu. Convergence to equilibrium for granular media equations and their Euler schemes. Ann. Appl. Probab. 13, 2 (2003), 540–560. Zbl1031.60085MR1970276
- H. P. McKean. Propagation of chaos for a class of non-linear parabolic equations. In Lecture Series in Differential Equations, Session 7, Catholic Univ., 1967. Zbl0181.44401
- S. Méléard. Asymptotic behaviour of some interacting particle systems ; McKean-Vlasov and Boltzmann models. Lecture Notes in Math. 1627, Springer, Berlin, 1996. Zbl0864.60077MR1431299
- H. Neunzert. An introduction to the nonlinear Boltzmann-Vlasov equation. Lecture Notes in Math. 1048. Springer, Berlin, 1984. Zbl0575.76120MR740721
- A.-S. Sznitman. Topics in propagation of chaos. Lecture Notes in Math. 1464, Springer, Berlin, 1991. Zbl0732.60114MR1108185
- D. Talay. Probabilistic numerical methods for partial differential equations : elements of analysis. Lecture Notes in Math. 1627, Springer, Berlin, 1996. Zbl0854.65116MR1431302
- T. Vicsek, A. Czirok, E. Ben-Jacob, I. Cohen et O. Shochet. Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75, (1995), 1226–1229.
- C. Villani.Optimal transport, old and new. Grundlehren der math. Wiss. 338, Springer, Berlin, 2009. Zbl1156.53003MR2459454
- C. Yates, R. Erban, C. Escudero, L. Couzin, J. Buhl, L. Kevrekidis, P. Maini et D. Sumpter. Inherent noise can facilitate coherence in collective swarm motion. Proc. Nat. Acad. Sci. 106, 14 (2009), 5464–5469.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.