METANOLIN
(METAstability for NOnLINear processes)

ANR-19-CE40-0009    2019 -- 2024

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Papers:

• Large Deviations and Exit-times for reflected McKean-Vlasov equations with self-stabilizing terms and superlinear drifts. Daniel Adams, Gonçalo dos Reis, Romain Ravaille, William Salkeld and Julian Tugaut. Stochastic Processes and their Applications.



• Reducing exit-times of diffusions with repulsive interactions. Paul-Éric Chaudru de Raynal, Hong Duong, Pierre Monmarché, Milica Tomašević and Julian Tugaut. ESAIM Probability and statistics.



• Self-interacting diffusions: long-time behaviour and exit-problem in the uniformly convex case. Ashot Aleksian, Pierre Del Moral, Aline Kurtzmann and Julian Tugaut. ESAIM Probability and statistics.



• Exit-problem for a class of non-Markov processes with path dependency. Ashot Aleksian, Aline Kurtzmann and Julian Tugaut. Revision in Probability Theory and Related Fields.



• Granular media equation with double-wells external landscape: limiting steady state. Julian Tugaut. Comptes Rendus de l'Académie des Sciences.



• Measure-dependent non-linear diffusions with superlinear drifts: asymptotic behaviour of the first exit-times. Ashot Aleksian and Julian Tugaut. To appear in Electronic Journal of Probability.



• Metastability for systems of interacting neurons. Eva Löcherbach and Pierre Monmarché. Annales de l'Institut Henri Poincaré.



• On the steady states for the granular media equation: existence, local uniqueness, local stability and rate of convergence. Julian Tugaut. Submitted (22 pages).



• Multi-species McKean-Vlasov dynamics. Hong Duong, Grigorios Pavliotis and Julian Tugaut. Writting in process (38 pages).



• A Kramers'type law for the first collision-time of two self-stabilizing diffusions and of their particle approximations. Jean-François Jabir and Julian Tugaut. Writting in process (42 pages).



• Competition between common noise and idiosyncratic noise in the small-noise limit for Ornstein-Uhlenbeck McKean-Vlasov diffusions: Large deviations principle and first hitting-times. Paul-Éric Chaudru de Raynal and Julian Tugaut. Writting in process (13 pages).