. Introduction, . Organization, and . Set-up,

J. A. Acebron, L. L. Bonilla, C. J. Vicente, F. Ritort, and R. Spigler, The Kuramoto model: A simple paradigm for synchronization phenomena, Reviews of Modern Physics, vol.77, issue.1, p.137185, 2005.

R. A. Adams and J. Fournier, Sobolev spaces. Number 65 in Pure and applied mathematics series, 2003.

N. Alon and A. Naor, Approximating the Cut-Norm via Grothendieck's Inequality, SIAM Journal on Computing, vol.35, p.787803, 2006.

A. Arenas, A. Diaz-guilera, J. Kurths, Y. Moreno, and C. Zhou, Synchronization in complex networks, Physics Reports, vol.469, issue.3, p.93153, 2008.

A. Basak, S. Bhamidi, S. Chakraborty, and A. Nobel, Large subgraphs in pseudo-random graphs, 2016.

E. Bayraktar, S. Chakraborty, and R. Wu, Graphon mean eld systems, p.2020

F. Bechtold, Strong solutions of semilinear SPDEs with unbounded diusion, p.2020

F. Bechtold and F. Coppini, A Law of Large Numbers for interacting diusions via a mild formulation, p.2020

L. Bertini, G. Giacomin, and K. Pakdaman, Dynamical aspects of mean eld plane rotators and the Kuramoto model, Journal of Statistical Physics, vol.138, issue.1-3, p.270290, 2010.

L. Bertini, G. Giacomin, and C. Poquet, Synchronization and random long time dynamics for mean-eld plane rotators. Probability Theory and Related Fields, vol.160, p.593653, 2014.

G. Bet, F. Coppini, and F. R. Nardi, Weakly interacting oscillators on dense random graphs, p.2020
URL : https://hal.archives-ouvertes.fr/hal-02870131

G. Bet, R. Van-der-hofstad, and J. S. Van-leeuwaarden, Big jobs arrive early: From critical queues to random graphs, 2017.

S. Bhamidi, A. Budhiraja, and R. Wu, Weakly interacting particle systems on inhomogeneous random graphs. Stochastic Processes and their Applications, vol.129, p.21742206, 2019.

P. Billingsley, Convergence of Probability Measures, 1999.

K. Bogerd, R. M. Castro, and R. Van-der-hofstad, Cliques in rank-1 random graphs: the role of inhomogeneity, 2018.

B. Bollobas and O. Riordan, Metrics for sparse graphs, Survey in combinatorics, vol.365, p.211287, 2009.

C. Borgs, J. Chayes, H. Cohn, and Y. Zhao, An L p theory of sparse graph convergence I: Limits, sparse random graph models, and power law distributions, Transactions of the American Mathematical Society, vol.372, issue.5, p.30193062, 2019.

C. Borgs, J. T. Chayes, H. Cohn, and Y. Zhao, An L p theory of sparse graph convergence II: LD convergence, quotients and right convergence, The Annals of Probability, vol.46, issue.1, p.337396, 2018.

S. Boucheron, G. Lugosi, and P. Massart, Concentration Inequalities: A Nonasymptotic Theory of Independence, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00794821

W. Braun and K. Hepp, The Vlasov dynamics and its uctuations in the 1/N limit of interacting classical particles, Communications in Mathematical Physics, vol.56, issue.2, p.101113, 1977.

J. V. Brecht, T. Kolokolnikov, A. L. Bertozzi, and H. Sun, Swarming on Random Graphs, Journal of Statistical Physics, p.150173, 2013.

H. Brezis, Analyse fonctionnelle : Théorie et applications. Dunod, 1999.

A. Budhiraja, P. Dupuis, and M. Fischer, Large deviation properties of weakly interacting processes via weak convergence methods. The Annals of Probability, vol.40, p.74102, 2012.

P. E. Caines and M. Huang, Graphon Mean Field Games and the GMFG Equations, IEEE Conference on Decision and Control (CDC), 2018.

R. Carmona, D. Cooney, C. Graves, and M. Lauriere, Stochastic Graphon Games: I. The Static Case, 2019.

J. Chevallier, A. Duarte, E. Löcherbach, and G. Ost, Mean eld limits for nonlinear spatially extended Hawkes processes with exponential memory kernels, Stochastic Processes and their Applications, vol.129, pp.1-27, 2019.

H. Chiba and G. S. Medvedev, The mean eld analysis of the kuramoto model on graphs i. the mean eld equation and transition point formulas, Discrete & Continuous Dynamical Systems -A, vol.39, issue.1, p.131, 2019.

F. R. Chung, R. L. Graham, and R. M. Wilson, Quasi-random graphs, Combinatorica, vol.9, issue.4, p.345362, 1989.

M. Coghi, J. Deuschel, P. Friz, and M. Maurelli, Pathwise McKean-Vlasov Theory with Additive Noise, 2019.

F. Coppini, Long time dynamics for interacting oscillators on graphs, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02263485

F. Coppini, H. Dietert, and G. Giacomin, A law of large numbers and large deviations for interacting diusions on Erd®sRényi graphs, Stochastics and Dynamics, vol.20, issue.02, p.2050010, 2020.

G. Da-prato and J. Zabczyk, Stochastic Equations in Innite Dimensions, Number 45 in Encyclopedia of Mathematics and its Applications, 2010.

P. Dai-pra and F. D. Hollander, McKean-Vlasov limit for interacting random processes in random media, Journal of Statistical Physics, vol.84, issue.3-4, p.735772, 1996.

D. A. Dawson and J. Gärtner, Large deviations from the mckean-vlasov limit for weakly interacting diusions, Stochastics, vol.20, p.247308, 1987.

V. H. De-la-pena, M. J. Klass, and T. L. Lai, Self-normalized processes: exponential inequalities, moment bounds and iterated logarithm laws, The Annals of Probability, vol.32, issue.3A, p.19021933, 2004.

S. Delattre, G. Giacomin, and E. Luçon, A Note on Dynamical Models on Random Graphs and Fokker-Planck Equations, Journal of Statistical Physics, vol.165, issue.4, p.785798, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01355715

A. Dembo and A. Montanari, Ising models on locally tree-like graphs, The Annals of Applied Probability, vol.20, issue.2, p.565592, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00290779

A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, volume 38 of Stochastic Modelling and Applied Probability, 2010.

F. Hollander, Large Deviations, 2000.

P. Diaconis and S. Janson, Graph limits and exchangeable random graphs, Rendiconti di Matematica, vol.28, p.3361, 2008.

R. L. Dobrushin, Vlasov equations. Functional Analysis and Its Applications, vol.13, p.115123, 1979.

P. Dupuis and R. S. Ellis, A Weak Convergence Approach to the Theory of Large Deviations, 2011.

F. Dörer and F. Bullo, Synchronization in complex networks of phase oscillators: A survey, Automatica, vol.50, issue.6, p.15391564, 2014.

J. Feng and T. G. Kurtz, Large Deviations for Stochastic Processes, Mathematical Surveys and Monographs, vol.131, 2006.

B. Fernandez and S. Méléard, A Hilbertian approach for uctuations on the McKean-Vlasov model, Stochastic Processes and their Applications, vol.71, p.3353, 1997.

F. Flandoli, M. Leimbach, and C. Olivera, Uniform convergence of proliferating particles to the FKPP equation, Journal of Mathematical Analysis and Applications, vol.473, issue.1, p.2752, 2019.

F. Flandoli, C. Olivera, and M. Simon, Uniform approximation of 2d Navier-Stokes equation by stochastic interacting particle systems, p.2020
URL : https://hal.archives-ouvertes.fr/hal-02529632

M. I. Freidlin and A. D. Wentzell, Random Perturbations of Dynamical Systems, Grundlehren der mathematischen Wissenschaften, vol.260, 1984.

P. K. Friz and M. Hairer, A Course on Rough Paths, 2014.

T. Funaki, A certain class of diusion processes associated with nonlinear parabolic equations. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.67, p.331348, 1984.

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, p.12471273, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00705301

S. E. Graversen and G. Peskir, Maximal inequalities for the Ornstein-Uhlenbeck process, Proceedings of the American Mathematical Society, vol.128, issue.10, p.30353042, 2000.

M. Gubinelli, Controlling rough paths, Journal of Functional Analysis, vol.216, issue.1, p.86140, 2004.

M. Gubinelli and S. Tindel, Rough evolution equations. The Annals of Probability, vol.38, p.175, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00359724

O. Guédon and R. Vershynin, Community detection in sparse networks via Grothendieck's inequality. Probability Theory and Related Fields, vol.165, p.10251049, 2016.

J. Gärtner, On the McKean-Vlasov Limit for Interacting Diusions, Mathematische Nachrichten, vol.137, issue.1, 1988.

E. Heiman, G. Schechtman, and A. Shraibman, Deterministic algorithms for matrix completion, Random Structures & Algorithms, vol.45, issue.2, p.306317, 2014.

D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, vol.840, 1981.

S. Hoory, N. Linial, and A. Wigderson, Expander graphs and their applications, Bulletin of the American Mathematical Society, vol.43, issue.04, p.439562, 2006.

N. Ikeda and S. Watanabe, Stochastic Dierential Equations and Diusion Processes, vol.24, 1989.

P. Jabin and Z. Wang, Quantitative estimates of propagation of chaos for stochastic systems with W ?1,? kernels. Inventiones mathematicae, vol.214, p.523591, 2018.

C. Jia and G. Zhao, Moderate maximal inequalities for the Ornstein-Uhlenbeck process, 2017.

M. Kac, Foundations of Kinetic Theory, Berkeley Symposium on Mathematical Statistics and Probability, 1956.

Y. Katznelson, An Introduction To Harmonic Analysis. Cambridge Mathematical Library, 2004.

V. N. Kolokoltsov, Number 38 in De Gruyter studies in mathematics, 2011.

V. Konarovskyi, T. Lehmann, and M. V. Renesse, Dean-Kawasaki dynamics: ill-posedness vs, triviality. Electronic Communications in Probability, vol.24, 2019.

V. Konarovskyi, T. Lehmann, and M. Von-renesse, On Dean-Kawasaki Dynamics with Smooth Drift Potential, Journal of Statistical Physics, 2019.

Y. Kuramoto, Self-entrainment of a population of coupled non-linear oscillators, International Symposium on Mathematical Problems in Theoretical Physics, number 39 in Lecture Notes in Physics, p.420422, 1975.

Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence, Springer Series in Synergetics, vol.19, 1984.

D. Lacker, K. Ramanan, and R. Wu, Large sparse networks of interacting diusions, 2019.

C. Lancellotti, On the Vlasov Limit for Systems of Nonlinearly Coupled Oscillators without Noise, Transport Theory and Statistical Physics, vol.34, p.523535, 2005.

C. M. Le, E. Levina, and R. Vershynin, Concentration and regularization of random graphs, Random Structures & Algorithms, vol.51, issue.3, p.538561, 2017.

L. Lovász, Large Networks and Graph Limits, vol.60, 2012.

L. Lovász and B. Szegedy, Limits of dense graph sequences, Journal of Combinatorial Theory, Series B, vol.96, issue.6, p.933957, 2006.

A. Lunardi, Analytic semigroups and optimal regularity in parabolic problems, Modern Birkhäuser classics. Birkhäuser, 2012.

E. Luçon, Quenched Large Deviations for Interacting Diusions in Random Media, Journal of Statistical Physics, vol.166, issue.6, p.14051440, 2017.

E. Luçon, Quenched asymptotics for interacting diusions on inhomogeneous random graphs. Stochastic Processes and their Applications, 2020.

E. Luçon and C. Poquet, Long time dynamics and disorder-induced traveling waves in the stochastic Kuramoto model, Probabilités et Statistiques, vol.53, issue.3, p.11961240, 2017.

E. Luçon and W. Stannat, Mean eld limit for disordered diusions with singular interactions, The Annals of Applied Probability, vol.24, issue.5, p.19461993, 2014.

C. Léonard, Une loi des grands nombres pour des systèmes de diusions avec interaction et à coecients non bornés, Annales de l'I.H.P. Probabilités et statistiques, vol.22, issue.2, p.237262, 1986.

H. P. Mckean, A class of Markov processes associated with nonlinear parabolic equations, Proceedings of the National Academy of Sciences of the United States of America, vol.56, p.19071911, 1966.

G. S. Medvedev, The continuum limit of the kuramoto model on sparse random graphs, 2018.

S. Mischler and C. Mouhot, Kac's Program in Kinetic Theory, Inventiones Mathematicae, vol.193, issue.1, p.1147, 2013.

S. Mischler, C. Mouhot, and B. Wennberg, A new approach to quantitative propagation of chaos for drift, diusion and jump processes. Probability Theory and Related Fields, vol.161, p.159, 2015.

S. Méléard, Asymptotic behaviour of some interacting particle systems; McKean-Vlasov and Boltzmann models, Probabilistic Models for Nonlinear Partial Dierential Equations, number 1627 in Lecture Notes in Mathematics, p.4295, 1996.

M. Métivier, Semimartingales, A Course on Stochastic Processes, De Gruyter Studies in Mathematics, vol.2, 1982.

H. Neunzert, An introduction to the nonlinear boltzmann-vlasov equation, Kinetic Theories and the Boltzmann Equation, p.60110, 1984.

K. Oelschläger, A Martingale Approach to the Law of Large Numbers for Weakly Interacting Stochastic Processes, The Annals of Probability, vol.12, issue.2, p.458479, 1984.

R. I. Oliveira, Concentration of the adjacency matrix and of the Laplacian in random graphs with independent edges, 2009.

R. I. Oliveira and G. H. Reis, Interacting Diusions on Random Graphs with Diverging Average Degrees: Hydrodynamics and Large Deviations, Journal of Statistical Physics, vol.176, issue.5, p.10571087, 2019.

R. I. Oliveira, G. H. Reis, and L. M. Stolerman, Interacting diusions on sparse graphs: hydrodynamics from local weak limits, 2018.

E. Olivieri and M. E. Vares, Large Deviations and Metastability, 2005.

G. Pisier, Grothendieck's Theorem, past and present, Bulletin of the American Mathematical Society, vol.49, issue.2, p.237323, 2012.

F. A. Rodrigues, T. K. Peron, P. Ji, and J. Kurths, The Kuramoto model in complex networks, Physics Reports, vol.610, 2016.

T. Shiga and H. Tanaka, Central limit theorem for a system of Markovian particles with mean eld interactions, vol.69, p.439459, 1985.

S. H. Strogatz, From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators, Physica D: Nonlinear Phenomena, vol.143, issue.1-4, p.120, 2000.

D. W. Stroock and S. R. Varadhan, Multidimensional diusion processes. Number 233 in Grundlehren der mathematischen Wissenschaften, 2006.

A. Sznitman, Topics in propagation of chaos, Ecole d'Eté de Probabilités de Saint-Flour XIX -1989, vol.1464, p.165251, 1991.

H. Tanaka, Limit Theorems for Certain Diusion Processes with Interaction, North-Holland Mathematical Library, vol.32, p.469488, 1984.

J. M. Van-neerven, M. C. Veraar, and L. Weis, Stochastic integration in UMD Banach spaces, The Annals of Probability, vol.35, issue.4, p.14381478, 2007.

K. Yosida, Functional Analysis. Classics in Mathematics, 1995.