A. Arnold, P. Markowich, G. Toscani, and A. Unterreiter, ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS, Communications in Partial Differential Equations, vol.324, issue.1-2, pp.43-100, 2001.
DOI : 10.1007/s002200050631

F. [. Bakry, P. Barthe, A. Cattiaux, and . Guillin, A simple proof of the Poincar?? inequality for a large class of probability measures, Electronic Communications in Probability, vol.13, issue.0, pp.60-66, 2008.
DOI : 10.1214/ECP.v13-1352

E. [. Benedetto, J. A. Caglioti, M. Carrillo, and . Pulvirenti, A non- Maxwellian steady distribution for one-dimensional granular media, J. Statist. Phys, vol.91, pp.5-6979, 1998.

B. [. Benachour, D. Roynette, P. Talay, and . Vallois, Nonlinear self-stabilizing processes ??? I Existence, invariant probability, propagation of chaos, Stochastic Processes and their Applications, vol.75, issue.2, pp.173-201, 1998.
DOI : 10.1016/S0304-4149(98)00018-0

B. [. Benachour, P. Roynette, and . Vallois, Nonlinear self-stabilizing processes . II. Convergence to invariant probability. Stochastic Process, Appl, vol.75, issue.2, pp.203-224, 1998.

A. [. Cattiaux, F. Guillin, and . Malrieu, Probabilistic approach for granular media equations in the non-uniformly convex case. Probab. Theory Related Fields, pp.19-40, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00021591

A. José, R. J. Carrillo, C. Mccann, and . Villani, Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates, Rev. Mat. Iberoamericana, vol.19, issue.3, pp.971-1018, 2003.

A. Dermoune, Propagation and conditional propagation of chaos for pressureless gas equations. Probab. Theory Related Fields, pp.459-476, 2003.

C. Graham, Nonlinear limit for a system of diffusing particles which alternate between two states, Applied Mathematics & Optimization, vol.28, issue.2, pp.75-90, 1990.
DOI : 10.1007/BF01447321

C. Graham, McKean-Vlasov Itô-Skorohod equations, and nonlinear diffusions with discrete jump sets. Stochastic Process, Appl, vol.40, issue.1, pp.69-82, 1992.

[. Herrmann, P. Imkeller, and D. Peithmann, Large deviations and a Kramers??? type law for self-stabilizing diffusions, The Annals of Applied Probability, vol.18, issue.4, pp.1379-1423, 2008.
DOI : 10.1214/07-AAP489
URL : https://hal.archives-ouvertes.fr/hal-00139965

R. Holley and D. Stroock, Logarithmic Sobolev inequalities and stochastic Ising models, Journal of Statistical Physics, vol.42, issue.5-6, pp.1159-1194, 1987.
DOI : 10.1007/BF01011161

]. S. Ht10a, J. Herrmann, and . Tugaut, Non-uniqueness of the invariant probabilities for self-stabilizing processes. Stochastic Process, Appl, vol.120, issue.7, pp.1215-1246, 2010.

]. S. Ht10b, J. Herrmann, and . Tugaut, Stationary measures for self-stabilizing processes: asymptotic analysis in the small noise limit, Electron. J. Probab, vol.15, pp.2087-2116, 2010.

J. [. Herrmann and . Tugaut, Self-stabilizing processes: uniqueness problem for stationary measures and convergence rate in the small-noise limit, ESAIM: Probability and Statistics, vol.16, 2012.
DOI : 10.1051/ps/2011152
URL : https://hal.archives-ouvertes.fr/hal-00599139

[. and F. Malrieu, Propagation of chaos and Poincaré inequalities for a system of particles interacting through their CDF, Ann. Appl. Probab, vol.18, issue.5, pp.1706-1736, 2008.

S. [. Karatzas and . Shreve, Brownian motion and stochastic calculus, 1991.

O. Kavian, G. Kerkyacharian, and B. Roynette, Some Remarks on Ultracontractivity, Journal of Functional Analysis, vol.111, issue.1, pp.155-196, 1993.
DOI : 10.1006/jfan.1993.1008

F. Malrieu, Logarithmic Sobolev inequalities for some nonlinear PDE's. Stochastic Process, Appl, vol.95, issue.1, pp.109-132, 2001.

[. Malrieu, Convergence to equilibrium for granular media equations and their Euler schemes, The Annals of Applied Probability, vol.13, issue.2, pp.540-560, 2003.
DOI : 10.1214/aoap/1050689593
URL : https://hal.archives-ouvertes.fr/hal-01282602

]. H. Mck67 and J. Mckean, Propagation of chaos for a class of non-linear parabolic equations, Stochastic Differential Equations (Lecture Series in Differential Equations, Session 7, pp.41-57, 1967.

S. Méléard, Asymptotic behaviour of some interacting particle systems; McKean-Vlasov and Boltzmann models, Probabilistic models for nonlinear partial differential equations (Montecatini Terme, pp.42-95, 1995.
DOI : 10.1007/BF01055714

K. Oelschläger, A law of large numbers for moderately interacting diffusion processes, Zeitschrift f??r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.52, issue.2, pp.279-322, 1985.
DOI : 10.1007/BF02450284

W. Daniel, S. R. Stroock, . Srinivasa, and . Varadhan, Multidimensional diffusion processes, of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 1979.

A. Sznitman, Topics in propagation of chaos, École d'Été de Probabilités de Saint-Flour XIX?1989, pp.165-251, 1991.
DOI : 10.1070/SM1974v022n01ABEH001689

Y. Tamura, On asymptotic behaviors of the solution of a nonlinear diffusion equation, J. Fac. Sci. Univ. Tokyo Sect. IA Math, vol.31, issue.1, pp.195-221, 1984.

Y. Tamura, Free energy and the convergence of distributions of diffusion processes of McKean type, J. Fac. Sci. Univ. Tokyo Sect. IA Math, vol.34, issue.2, pp.443-484, 1987.

]. J. Tug10 and . Tugaut, Convergence to the equilibria for self-stabilizing processes in double well landscape. To appear in The Annals of Probability available on http, 2010.

J. Tugaut, Phase transitions of McKean???Vlasov processes in double-wells landscape, Stochastics An International Journal of Probability and Stochastic Processes, vol.34, issue.2, 2011.
DOI : 10.1214/aoap/1050689593
URL : https://hal.archives-ouvertes.fr/hal-00573046

J. Tugaut, Self-stabilizing processes in multi-wells landscape in R d -Invariant probabilities, 2011.

]. A. Ver06, . Yu, and . Veretennikov, On ergodic measures for McKean-Vlasov stochastic equations. In Monte Carlo and quasi-Monte Carlo methods, pp.471-486, 2004.