L. Ambrosio, N. Gigli, and G. Savaré, Gradient flows in metric spaces and in the space of probability measures, Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, 2008.

A. D. Banner, R. Fernholz, and I. Karatzas, Atlas models of equity markets, Ann. Appl. Probab, vol.15, issue.4, pp.2296-2330, 2005.
DOI : 10.1214/105051605000000449

URL : https://doi.org/10.1214/105051605000000449

S. Benachour, B. Roynette, D. Talay, and P. Vallois, Nonlinear self-stabilizing processes. I. Existence, invariant probability, propagation of chaos, Stochastic Process. Appl, vol.75, issue.2, pp.173-201, 1998.

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

D. Benedetto, E. Caglioti, J. A. Carrillo, and M. Pulvirenti, A non-Maxwellian steady distribution for one-dimensional granular media, J. Statist. Phys, vol.91, issue.5-6, pp.979-990, 1998.

D. Benedetto, E. Caglioti, and M. Pulvirenti, A kinetic equation for granular media, RAIRO Modél. Math. Anal. Numér, vol.31, issue.5, pp.615-641, 1997.
DOI : 10.1051/m2an:1999118

URL : https://www.esaim-m2an.org/articles/m2an/pdf/1999/02/m2an682.pdf

P. Billingsley, Convergence of probability measures. Wiley Series in Probability and Statistics: Probability and Statistics, 1999.

S. Bobkov and M. Ledoux, One-dimensional empirical measures, order statistics and Kantorovich transport distances. To appear in Mem

M. Bossy and D. Talay, Convergence rate for the approximation of the limit law of weakly interacting particles: application to the Burgers equation, Ann. Appl. Probab, vol.6, issue.3, pp.818-861, 1996.
URL : https://hal.archives-ouvertes.fr/inria-00074265

M. Bossy and D. Talay, A stochastic particle method for the McKean-Vlasov and the Burgers equation, Math. Comp, vol.66, issue.217, pp.157-192, 1997.
DOI : 10.1090/s0025-5718-97-00776-x

URL : https://www.ams.org/mcom/1997-66-217/S0025-5718-97-00776-X/S0025-5718-97-00776-X.pdf

C. Bruggeman, Dynamics of large rank-based systems of interacting diffusions, 2016.

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, vol.19, issue.3, pp.971-1018, 2003.
DOI : 10.4171/rmi/376

J. A. Carrillo, R. J. Mccann, and C. Villani, Contractions in the 2-Wasserstein length space and thermalization of granular media, Arch. Ration. Mech. Anal, vol.179, issue.2, pp.217-263, 2006.

P. Cattiaux, A. Guillin, and F. Malrieu, Probabilistic approach for granular media equations in the non-uniformly convex case, Probab. Theory Related Fields, vol.140, issue.1-2, pp.19-40, 2008.
DOI : 10.1007/s00440-007-0056-3

URL : https://hal.archives-ouvertes.fr/hal-00021591

P. Cattiaux and L. Pédeches, The 2-D stochastic Keller-Segel particle model: existence and uniqueness, ALEA, Lat. Am. J. Probab. Math. Stat, vol.13, issue.1, pp.447-463, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01263156

D. Chafaï, N. Gozlan, and P. Zitt, First-order global asymptotics for confined particles with singular pair repulsion, Ann. Appl. Probab, vol.24, issue.6, pp.2371-2413, 2014.

S. Chatterjee and S. Pal, A phase transition behavior for Brownian motions interacting through their ranks, vol.147, pp.123-159, 2010.
DOI : 10.1007/s00440-009-0203-0

URL : http://arxiv.org/pdf/0706.3558

D. A. Dawson and J. Gärtner, Large deviations and tunnelling for particle systems with mean field interaction, C. R. Math. Rep. Acad. Sci. Canada, vol.8, issue.6, pp.387-392, 1986.

D. A. Dawson and J. Gärtner, Large deviations from the McKean-Vlasov limit for weakly interacting diffusions, Stochastics, vol.20, issue.4, pp.247-308, 1987.

D. A. Dawson and J. Gärtner, Large deviations, free energy functional and quasi-potential for a mean field model of interacting diffusions, Mem. Amer. Math. Soc, vol.78, issue.398, p.94, 1989.
DOI : 10.1090/memo/0398

A. Dembo, M. Shkolnikov, S. R. Varadhan, and O. Zeitouni, Large deviations for diffusions interacting through their ranks, Comm. Pure Appl. Math, vol.69, issue.7, pp.1259-1313, 2016.

A. Dembo and O. Zeitouni, Large deviations techniques and applications, Stochastic Modelling and Applied Probability, vol.38, 2010.

P. Dupuis and R. S. Ellis, A weak convergence approach to the theory of large deviations, Wiley Series in Probability and Statistics: Probability and Statistics, 1997.

P. Dupuis, V. Laschos, and K. Ramanan, Large deviations for empirical measures generated by Gibbs measures with singular energy functionals, 2015.

R. S. Ellis, Entropy, large deviations, and statistical mechanics, Grundlehren der Mathematischen Wissenschaften, vol.271

. Springer-verlag, , 1985.

R. Fernholz, Stochastic portfolio theory, Stochastic Modelling and Applied Probability, vol.48, 2002.

J. Fouque and L. Sun, Systemic risk illustrated. Handbook on Systemic Risk, pp.444-452, 2013.

N. Fournier and B. Jourdain, Stochastic particle approximation of the Keller-Segel equation and two-dimensional generalization of Bessel processes, Ann. Appl. Probab, vol.27, issue.5, pp.2807-2861, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01171481

R. Jordan, D. Kinderlehrer, and F. Otto, The variational formulation of the Fokker-Planck equation, SIAM J. Math. Anal, vol.29, issue.1, pp.1-17, 1998.

B. Jourdain 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.

B. Jourdain, Diffusion processes associated with nonlinear evolution equations for signed measures, Methodol. Comput. Appl. Probab, vol.2, issue.1, pp.69-91, 2000.

B. Jourdain and J. Reygner, Propogation of chaos for rank-based interacting diffusions and long time behaviour of a scalar quasilinear parabolic equation, Stoch. Partial Differ. Equ. Anal. Comput, vol.1, issue.3, pp.455-506, 2013.

B. Jourdain and J. Reygner, Capital distribution and portfolio performance in the mean-field Atlas model, Ann. Finance, vol.11, issue.2, pp.151-198, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00921151

P. Kolli and M. Shkolnikov, SPDE limit of the global fluctuations in rank-based models, 2016.

T. Leblé and S. Serfaty, Large deviation principle for empirical fields of Log and Riesz Gases, 2015.

C. Léonard, Large deviations and law of large numbers for a mean field type interacting particle system, Stochastic Process. Appl, vol.25, issue.2, pp.215-235, 1987.

F. Malrieu, Convergence to equilibrium for granular media equations and their Euler schemes, Ann. Appl. Probab, vol.13, issue.2, pp.540-560, 2003.
URL : https://hal.archives-ouvertes.fr/hal-01282602

C. Mukherjee and S. R. Varadhan, Brownian occupation measures, compactness and large deviations, Ann. Probab, vol.44, issue.6, pp.3934-3964, 2016.

F. Otto, The geometry of dissipative evolution equations: the porous medium equation, Comm. Partial Differential Equations, vol.26, issue.1-2, pp.101-174, 2001.

S. Pal and J. Pitman, One-dimensional Brownian particle systems with rank-dependent drifts, Ann. Appl. Probab, vol.18, issue.6, pp.2179-2207, 2008.

L. Rey-bellet and K. Spiliopoulos, Irreversible Langevin samplers and variance reduction: a large deviations approach, Nonlinearity, vol.28, issue.7, pp.2081-2103, 2015.
DOI : 10.1088/0951-7715/28/7/2081

URL : http://arxiv.org/pdf/1404.0105

J. Reygner, Long time behaviour and mean-field limit of Atlas models, 2017.
DOI : 10.1051/proc/201760132

URL : https://hal.archives-ouvertes.fr/hal-01525360

J. Reygner, Chaoticity of the stationary distribution of rank-based interacting diffusions. Electron, Commun. Probab, vol.20, pp.1-20, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01056364

M. Shkolnikov, Large systems of diffusions interacting through their ranks, Stochastic Process. Appl, vol.122, issue.4, pp.1730-1747, 2012.
DOI : 10.1016/j.spa.2012.01.011

URL : https://doi.org/10.1016/j.spa.2012.01.011

C. Villani, Optimal transport, Grundlehren der Mathematischen Wissenschaften, vol.338
URL : https://hal.archives-ouvertes.fr/hal-00923320

. Springer-verlag, Old and new, 2009.

R. Wang, X. Wang, and L. Wu, Sanov's theorem in the Wasserstein distance: a necessary and sufficient condition, Statist. Probab. Lett, vol.80, pp.505-512, 2010.
DOI : 10.1016/j.spl.2009.12.003

U. Paris-est, CERMICS (ENPC)