J. A. Acebrón and L. L. Bonilla, Asymptotic description of transients and synchronized states of globally coupled oscillators, Physica D: Nonlinear Phenomena, vol.114, issue.3-4, pp.3-4296, 1998.
DOI : 10.1016/S0167-2789(97)00197-8

J. A. Acebrón, L. L. Bonilla, C. J. Pérez-vicente, F. Ritort, and R. Spigler, The Kuramoto model: A simple paradigm for synchronization phenomena, Reviews of Modern Physics, vol.77, issue.1, pp.137-185, 2005.
DOI : 10.1103/RevModPhys.77.137

R. A. Adams and J. J. Fournier, Sobolev spaces, Pure and Applied Mathematics, vol.140, 2003.

D. G. Aronsonann and . Norm, Addendum Non-negative solutions of linear parabolic equations, Sup. Pisa Ann. Scuola Norm. Sup. Pisa, vol.22, issue.25, pp.607-694221, 1968.

P. B. Bailey, W. N. Everitt, and A. Zettl, Regular and singular Sturm???Liouville problems with coupled boundary conditions, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.1, issue.03, pp.505-514, 1996.
DOI : 10.1112/plms/s3-64.3.545

N. J. Balmforth and R. Sassi, A shocking display of synchrony, Physica D: Nonlinear Phenomena, vol.143, issue.1-4, pp.21-55, 2000.
DOI : 10.1016/S0167-2789(00)00095-6

N. Berglund, B. Fernandez, and B. Gentz, Metastability in interacting nonlinear stochastic differential equations: I. From weak coupling to synchronization, Nonlinearity, vol.20, issue.11, pp.2551-2581, 2007.
DOI : 10.1088/0951-7715/20/11/006
URL : https://hal.archives-ouvertes.fr/hal-00115416

N. Berglund, B. Fernandez, and B. Gentz, behaviour, Nonlinearity, vol.20, issue.11, pp.2583-2614, 2007.
DOI : 10.1088/0951-7715/20/11/007
URL : https://hal.archives-ouvertes.fr/hal-00115417

L. Bertini, G. Giacomin, and K. Pakdaman, Dynamical Aspects of Mean Field Plane Rotators and??the??Kuramoto Model, Journal of Statistical Physics, vol.63, issue.3, pp.270-290, 2010.
DOI : 10.1007/s10955-009-9908-9
URL : https://hal.archives-ouvertes.fr/hal-00497541

P. Billingsley, Probability and measure. Wiley Series in Probability and Mathematical Statistics, 1995.

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

E. Bolthausen, Laplace approximations for sums of independent random vectors, pp.305-318, 1986.

L. L. Bonilla, J. C. Neu, and R. Spigler, Nonlinear stability of incoherence and collective synchronization in a population of coupled oscillators, Journal of Statistical Physics, vol.20, issue.1-2, pp.313-330, 1992.
DOI : 10.1007/BF01049037

L. L. Bonilla, C. J. Vicente, and R. Spigler, Time-periodic phases in populations of nonlinearly coupled oscillators with bimodal frequency distributions, Physica D: Nonlinear Phenomena, vol.113, issue.1, pp.79-97, 1998.
DOI : 10.1016/S0167-2789(97)00187-5

M. Bossy and D. Talay, A stochastic particle method for the McKean-Vlasov and the Burgers equation, Mathematics of Computation, vol.66, issue.217, pp.157-192, 1997.
DOI : 10.1090/S0025-5718-97-00776-X

A. Bovier, Statistical mechanics of disordered systems. Cambridge Series in Statistical and Probabilistic Mathematics, 2006.

H. Brezis, Analyse fonctionnelle Collection Mathématiques Appliquées pour la Maîtrise. [Collection of Applied Mathematics for the Master's Degree], Théorie et applications. [Theory and applications], 1983.

J. Buck, Synchronous Rhythmic Flashing of Fireflies. II., The Quarterly Review of Biology, vol.63, issue.3, pp.265-289, 1988.
DOI : 10.1086/415929

A. Budhiraja, P. Dupuis, and F. Markus, Large deviation properties of weakly interacting processes via weak convergence methods, The Annals of Probability, vol.40, issue.1
DOI : 10.1214/10-AOP616

R. Cerf, On Cramér's theory in infinite dimensions, of Panoramas et Synthèses [Panoramas and Syntheses]. Société Mathématique de France, 2007.

M. Y. Choi, H. J. Kim, D. Kim, and H. Hong, Synchronization in a system of globally coupled oscillators with time delay, Physical Review E, vol.61, issue.1, pp.371-381, 2000.
DOI : 10.1103/PhysRevE.61.371

F. Collet, The impact of disorder in the critical dynamics of mean-field models, 2009.

F. Collet and P. Dai-pra, The role of disorder in the dynamics of critical fluctuations of mean field models, Electronic Journal of Probability, vol.17, issue.0
DOI : 10.1214/EJP.v17-1896

F. Collet, P. Dai-pra, and E. Sartori, A Simple Mean Field Model for Social Interactions: Dynamics, Fluctuations, Criticality, Journal of Statistical Physics, vol.72, issue.8, pp.820-858, 2010.
DOI : 10.1007/s10955-010-9964-1

G. Da-prato and J. Zabczyk, Stochastic equations in infinite dimensions, volume 44 of Encyclopedia of Mathematics and its Applications, 1992.

D. Pra and F. Hollander, McKean-Vlasov limit for interacting random processes in random media, Journal of Statistical Physics, vol.56, issue.3-4, pp.3-4735, 1996.
DOI : 10.1007/BF02179656

D. A. Dawson, Critical dynamics and fluctuations for a mean-field model of cooperative behavior, Journal of Statistical Physics, vol.11, issue.1, pp.29-85, 1983.
DOI : 10.1007/BF01010922

A. Dembo and O. Zeitouni, Large deviations techniques and applications, Applications of Mathematics, vol.38, 1998.
DOI : 10.1007/978-1-4612-5320-4

F. Hollander, Large deviations, volume 14 of Fields Institute Monographs, 2000.

F. Hollander, Random polymers, volume 1974 of Lecture Notes in Mathematics, Lectures from the 37th Probability Summer School held in Saint-Flour, 2007.

R. M. Dudley, Convergence of Baire measures, Studia Math, vol.27, pp.251-268, 1966.

N. Dunford, J. T. Schwartz-william, G. Bade, and R. G. Bartle, Linear operators. Part II. Wiley Classics Library Spectral theory, 1988.

N. Dunford, J. T. Schwartz-william, G. Bade, and R. G. Bartle, Linear operators. Part III. Wiley Classics Library Spectral operators, 1988.

M. S. Eastham, Results and problems in the spectral theory of periodic differential equations, Spectral theory and differential equations (Proc. Sympos., Dundee, pp.126-135, 1974.
DOI : 10.1016/0022-0396(72)90069-1

B. Fernandez and S. Méléard, A Hilbertian approach for fluctuations on the McKean- Vlasov model. Stochastic Process, Appl, vol.71, issue.1, pp.33-53, 1997.

A. Friedman, Partial differential equations of parabolic type, N.J, 1964.

J. Gärtner, On the McKean-Vlasov Limit for Interacting Diffusions, Mathematische Nachrichten, vol.44, issue.1, pp.197-248, 1988.
DOI : 10.1002/mana.19881370116

G. Giacomin, Disorder and critical phenomena through basic probability models Lecture notes from the 40th Probability Summer School held in Saint-Flour, Lecture Notes in Mathematics, vol.2025, 2010.

G. Giacomin, E. Luçon, and C. Poquet, Coherence Stability and Effect of Random Natural Frequencies in Populations of Coupled Oscillators, Journal of Dynamics and Differential Equations, vol.63, issue.2
DOI : 10.1007/s10884-014-9370-5
URL : https://hal.archives-ouvertes.fr/hal-01018542

G. Giacomin, K. Pakdaman, and X. Pellegrin, Global attractor and asymptotic dynamics in the Kuramoto model for coupled noisy phase oscillators, Nonlinearity, vol.25, issue.5
DOI : 10.1088/0951-7715/25/5/1247
URL : https://hal.archives-ouvertes.fr/hal-00705301

G. Giacomin, K. Pakdaman, X. Pellegrin, and C. Poquet, Transitions in Active Rotator Systems: Invariant Hyperbolic Manifold Approach, SIAM Journal on Mathematical Analysis, vol.44, issue.6
DOI : 10.1137/110846452
URL : https://hal.archives-ouvertes.fr/hal-00783567

G. R. Grimmett and D. R. Stirzaker, Probability and random processes, 2001.

D. Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics, vol.840, 1981.
DOI : 10.1007/BFb0089647

M. W. Hirsch, C. C. Pugh, and M. Shub, Invariant manifolds, Lecture Notes in Mathematics, vol.583, 1977.

M. Hitsuda and I. Mitoma, Tightness problem and stochastic evolution equation arising from fluctuation phenomena for interacting diffusions, Journal of Multivariate Analysis, vol.19, issue.2, pp.311-328, 1986.
DOI : 10.1016/0047-259X(86)90035-7

B. Jourdain and F. Malrieu, Propagation of chaos and Poincar?? inequalities for a system of particles interacting through their cdf, The Annals of Applied Probability, vol.18, issue.5, pp.1706-1736, 2008.
DOI : 10.1214/07-AAP513

B. Jourdain and S. Méléard, Propagation of chaos and fluctuations for a moderate model with smooth initial data, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.34, issue.6, pp.727-766, 1998.
DOI : 10.1016/S0246-0203(99)80002-8

I. Karatzas and S. E. Shreve, Brownian motion and stochastic calculus, Graduate Texts in Mathematics, vol.113, 1991.
DOI : 10.1007/978-1-4612-0949-2

T. Kato, Perturbation theory for linear operators, Classics in Mathematics, 1995.
DOI : 10.1007/978-3-662-12678-3

S. Y. Kourtchatov, V. V. Likhanskii, A. P. Napartovich, F. T. Arecchi, and A. Lapucci, Theory of phase locking of globally coupled laser arrays, Physical Review A, vol.52, issue.5, pp.4089-4094, 1995.
DOI : 10.1103/PhysRevA.52.4089

Y. Kuramoto, Self-entrainment of a population of coupled non-linear oscillators, International Symposium on Mathematical Problems in Theoretical Physics, pp.420-422, 1975.
DOI : 10.1007/BFb0013365

J. Gall, Mouvement brownien et calcul stochastique, 1996.

E. Luçon, Quenched Limits and Fluctuations of the Empirical Measure for Plane Rotators in Random Media., Electronic Journal of Probability, vol.16, issue.0, pp.792-829, 2011.
DOI : 10.1214/EJP.v16-874

E. Luçon, Large-time asymptotics for the fluctuation SPDE in the Kuramoto synchronization model, 2012.

F. 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

A. S. Markus, Introduction to the spectral theory of polynomial operator pencils, volume 71 of Translations of Mathematical Monographs, Translated from the Russian by H. H. McFaden, 1988.

H. P. Mckean and J. , 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 and S. Roelly, Sur les convergences étroite ou vague de processus à valeurs mesures, C. R. Acad. Sci. Paris Sér. I Math, issue.8, pp.317785-788, 1993.

D. Michaels, E. Matyas, and J. Jalife, Mechanisms of sinoatrial pacemaker synchronization: a new hypothesis, Circulation Research, vol.61, issue.5, pp.704-714, 1987.
DOI : 10.1161/01.RES.61.5.704

I. Mitoma, Tightness of Probabilities On $C(\lbrack 0, 1 \rbrack; \mathscr{Y}')$ and $D(\lbrack 0, 1 \rbrack; \mathscr{Y}')$, The Annals of Probability, vol.11, issue.4, pp.989-999, 1983.
DOI : 10.1214/aop/1176993447

M. Möller and A. Zettl, Symmetrical Differential Operators and Their Friedrichs Extension, Journal of Differential Equations, vol.115, issue.1, pp.50-69, 1995.
DOI : 10.1006/jdeq.1995.1003

Y. Nakamura, F. Tominaga, and T. Munakata, Clustering behavior of time-delayed nearest-neighbor coupled oscillators, Physical Review E, vol.49, issue.6, pp.4849-4856, 1994.
DOI : 10.1103/PhysRevE.49.4849

Z. Neda, E. Ravasz, Y. Brechet, T. Vicsek, and A. Barabasi, Self-organizing processes: The sound of many hands clapping, Nature, vol.403, issue.6772, pp.849-850, 2000.
DOI : 10.1038/35002660

K. Oelschläger, A Martingale Approach to the Law of Large Numbers for Weakly Interacting Stochastic Processes, The Annals of Probability, vol.12, issue.2, pp.458-479, 1984.
DOI : 10.1214/aop/1176993301

F. Otto and M. Westdickenberg, Eulerian Calculus for the Contraction in the Wasserstein Distance, SIAM Journal on Mathematical Analysis, vol.37, issue.4, pp.1227-1255, 2005.
DOI : 10.1137/050622420

A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, vol.44, 1983.
DOI : 10.1007/978-1-4612-5561-1

P. A. Pearce, Mean-field bounds on the magnetization for ferromagnetic spin models, Journal of Statistical Physics, vol.27, issue.2, pp.309-320, 1981.
DOI : 10.1007/BF01022189

H. Risken, The Fokker-Planck equation, volume 18 of Springer Series in Synergetics, Methods of solution and applications, 1989.

S. Roelly-coppoletta, A criterion of convergence of measure???valued processes: application to measure branching processes, Stochastics, vol.8, issue.1-2, pp.43-65, 1986.
DOI : 10.1007/BF00736006

H. L. Royden, Real analysis, 1988.

H. Sakaguchi, Cooperative Phenomena in Coupled Oscillator Systems under External Fields, Progress of Theoretical Physics, vol.79, issue.1, pp.39-46, 1988.
DOI : 10.1143/PTP.79.39

H. Sakaguchi and Y. Kuramoto, A Soluble Active Rotater Model Showing Phase Transitions via Mutual Entertainment, Progress of Theoretical Physics, vol.76, issue.3, pp.576-581, 1986.
DOI : 10.1143/PTP.76.576

H. Sakaguchi, S. Shinomoto, and Y. Kuramoto, Local and grobal self-entrainments in oscillator lattices. Progress of Theoretical Physics, pp.1005-1010, 1987.

H. Sakaguchi, S. Shinomoto, and Y. Kuramoto, Phase Transitions and Their Bifurcation Analysis in a Large Population of Active Rotators with Mean-Field Coupling, Progress of Theoretical Physics, vol.79, issue.3, pp.600-607, 1988.
DOI : 10.1143/PTP.79.600

G. R. Sell and Y. You, Dynamics of evolutionary equations, Applied Mathematical Sciences, vol.143, 2002.
DOI : 10.1007/978-1-4757-5037-9

T. Shiga and H. Tanaka, Central limit theorem for a system of Markovian particles with mean field interactions, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.11, issue.3, pp.439-459, 1985.
DOI : 10.1007/BF00532743

S. Shinomoto and Y. Kuramoto, Phase Transitions in Active Rotator Systems, Progress of Theoretical Physics, vol.75, issue.5, pp.1105-1110, 1986.
DOI : 10.1143/PTP.75.1105
URL : http://ptp.oxfordjournals.org/cgi/content/short/75/5/1105

R. E. Showalter, Monotone operators in Banach space and nonlinear partial differential equations, volume 49 of Mathematical Surveys and Monographs, 1997.

S. H. Strogatz, From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators, Bifurcations, patterns and symmetry, pp.1-20, 2000.
DOI : 10.1016/S0167-2789(00)00094-4

S. H. Strogatz and R. E. Mirollo, Collective synchronisation in lattices of nonlinear oscillators with randomness, Journal of Physics A: Mathematical and General, vol.21, issue.13, pp.699-705, 1988.
DOI : 10.1088/0305-4470/21/13/005

S. H. Strogatz and R. E. Mirollo, Phase-locking and critical phenomena in lattices of coupled nonlinear oscillators with random intrinsic frequencies, Physica D: Nonlinear Phenomena, vol.31, issue.2, pp.31143-168, 1988.
DOI : 10.1016/0167-2789(88)90074-7

S. H. Strogatz and R. E. Mirollo, Stability of incoherence in a population of coupled oscillators, Journal of Statistical Physics, vol.60, issue.3-4, pp.3-4613, 1991.
DOI : 10.1007/BF01029202

S. H. Strogatz, R. E. Mirollo, and P. C. Matthews, Coupled nonlinear oscillators below the synchronization threshold: Relaxation by generalized Landau damping, Physical Review Letters, vol.68, issue.18, pp.2730-2733, 1992.
DOI : 10.1103/PhysRevLett.68.2730

A. Sznitman, Nonlinear reflecting diffusion process, and the propagation of chaos and fluctuations associated, Journal of Functional Analysis, vol.56, issue.3, pp.311-336, 1984.
DOI : 10.1016/0022-1236(84)90080-6

A. Sznitman, Topics in propagation of chaos, Lecture Notes in Math, vol.22, issue.1, pp.165-251, 1991.
DOI : 10.1070/SM1974v022n01ABEH001689

D. Talay and O. Vaillant, Vitesse de convergence d'une m??thode particulaire stochastique avec poids d'interaction al??atoires, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.330, issue.9, pp.821-824, 2000.
DOI : 10.1016/S0764-4442(00)00265-2

D. Talay and O. Vaillant, A stochastic particle method with random weights for the computation of statistical solutions of McKean-Vlasov equations, The Annals of Applied Probability, vol.13, issue.1, pp.140-180, 2003.
DOI : 10.1214/aoap/1042765665
URL : https://hal.archives-ouvertes.fr/inria-00072260

T. To, M. A. Henson, E. D. Herzog, and F. J. Iii, A Molecular Model for Intercellular Synchronization in the Mammalian Circadian Clock, Biophysical Journal, vol.92, issue.11, pp.923792-3803, 2007.
DOI : 10.1529/biophysj.106.094086

G. Wainrib, Randomness in neurons : a multiscale probabilistic analysis, 2010.

T. J. Walker, Acoustic Synchrony: Two Mechanisms in the Snowy Tree Cricket, Science, vol.166, issue.3907, pp.891-894, 1969.
DOI : 10.1126/science.166.3907.891

M. K. Yeung and S. H. Strogatz, Time Delay in the Kuramoto Model of Coupled Oscillators, Physical Review Letters, vol.82, issue.3, pp.648-651, 1999.
DOI : 10.1103/PhysRevLett.82.648

O. Zeitouni, Part II: Random Walks in Random Environment, Lectures on probability theory and statistics, pp.189-312, 2004.
DOI : 10.1007/978-3-540-39874-5_2