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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 86, 2014 - Issue 2
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Original Articles

Phase transitions of McKean–Vlasov processes in double-wells landscape

Julian TugautFakultät für Mathematik, Universität Bielefeld, D-33615Bielefeld, GermanyCorrespondence[email protected]
Pages 257-284 | Received 14 Oct 2011, Accepted 05 Feb 2013, Published online: 11 Mar 2013

Citations (30)

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Manh Hong Duong & Julian Tugaut. (2020) Coupled McKean–Vlasov diffusions: wellposedness, propagation of chaos and invariant measures. Stochastics 92:6, pages 900-943.
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Articles from other publishers (29)

L. Angeli, J. Barré, M. Kolodziejczyk & M. Ottobre. (2023) Well-posedness and stationary solutions of McKean-Vlasov (S)PDEs. Journal of Mathematical Analysis and Applications 526:2, pages 127301.
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Louis Sharrock, Nikolas Kantas, Panos Parpas & Grigorios A. Pavliotis. (2023) Online parameter estimation for the McKean–Vlasov stochastic differential equation. Stochastic Processes and their Applications 162, pages 481-546.
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Yao Liu, Yingchao Xie & Mengge Zhang. (2023) Phase Transitions for a Class of Time-Inhomogeneous Diffusion Processes. Journal of Statistical Physics 190:3.
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Bertram Tschiderer & Lane Chun Yeung. (2023) A trajectorial approach to relative entropy dissipation of McKean–Vlasov diffusions: Gradient flows and HWBI inequalities. Bernoulli 29:1.
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José A. Carrillo, Rishabh S. Gvalani & Jeremy S.-H. Wu. (2023) An invariance principle for gradient flows in the space of probability measures. Journal of Differential Equations 345, pages 233-284.
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Shao-Qin Zhang. (2023) Uniqueness of stationary distribution and exponential convergence for distribution dependent SDEs. Discrete and Continuous Dynamical Systems - S 0:0, pages 0-0.
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Pierre Monmarché. (2023) Elementary coupling approach for non-linear perturbation of Markov processes with mean-field jump mechanisms and related problems. ESAIM: Probability and Statistics 27, pages 278-323.
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Maximiliano Altamirano, Roberto Cortez, Matthieu Jonckheere & Lasse Leskelä. (2022) Persistence in a large network of sparsely interacting neurons. Journal of Mathematical Biology 86:1.
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Grigorios A. Pavliotis & Andrea Zanoni. (2022) Eigenfunction Martingale Estimators for Interacting Particle Systems and Their Mean Field Limit. SIAM Journal on Applied Dynamical Systems 21:4, pages 2338-2370.
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MATT BARKER, PIERRE DEGOND & MARIE-THERESE WOLFRAM. (2020) Comparing the best-reply strategy and mean-field games: The stationary case. European Journal of Applied Mathematics 33:1, pages 79-110.
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Louis-Pierre Chaintron & Antoine Diez. (2022) Propagation of chaos: A review of models, methods and applications. Ⅱ. Applications. Kinetic and Related Models 15:6, pages 1017.
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José A. Carrillo & Rishabh S. Gvalani. (2021) Phase Transitions for Nonlinear Nonlocal Aggregation-Diffusion Equations. Communications in Mathematical Physics 382:1, pages 485-545.
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Julian Tugaut. (2021) Captivity of the solution to the granular media equation. Kinetic & Related Models 14:2, pages 199.
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Xingyu Li. (2021) Phase Transition and Asymptotic Behavior of Flocking Cucker--Smale Model. Multiscale Modeling & Simulation 19:4, pages 1760-1783.
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Rishabh S. Gvalani & André Schlichting. (2020) Barriers of the McKean–Vlasov energy via a mountain pass theorem in the space of probability measures. Journal of Functional Analysis 279:11, pages 108720.
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Julio Backhoff, Giovanni Conforti, Ivan Gentil & Christian Léonard. (2020) The mean field Schrödinger problem: ergodic behavior, entropy estimates and functional inequalities. Probability Theory and Related Fields 178:1-2, pages 475-530.
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Mihaï Bostan & José Antonio Carrillo. (2020) Fluid models with phase transition for kinetic equations in swarming. Mathematical Models and Methods in Applied Sciences 30:10, pages 2023-2065.
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J. Barré, C. Bernardin, R. Chétrite, Y. Chopra & M. Mariani. (2020) From Fluctuating Kinetics to Fluctuating Hydrodynamics: A $$\Gamma $$-Convergence of Large Deviations Functionals Approach. Journal of Statistical Physics 180:1-6, pages 1095-1127.
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Eric Luçon & Christophe Poquet. (2019) Emergence of Oscillatory Behaviors for Excitable Systems with Noise and Mean-Field Interaction: A Slow-Fast Dynamics Approach. Communications in Mathematical Physics 373:3, pages 907-969.
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S. N. Gomes, G. A. Pavliotis & U. Vaes. (2020) Mean Field Limits for Interacting Diffusions with Colored Noise: Phase Transitions and Spectral Numerical Methods. Multiscale Modeling & Simulation 18:3, pages 1343-1370.
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José A. Carrillo, Serafim Kalliadasis, Sergio P. Perez & Chi-Wang Shu. (2020) Well-Balanced Finite-Volume Schemes for Hydrodynamic Equations with General Free Energy. Multiscale Modeling & Simulation 18:1, pages 502-541.
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J. A. Carrillo, R. S. Gvalani, G. A. Pavliotis & A. Schlichting. (2019) Long-Time Behaviour and Phase Transitions for the Mckean–Vlasov Equation on the Torus. Archive for Rational Mechanics and Analysis 235:1, pages 635-690.
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Susana N. Gomes, Serafim Kalliadasis, Grigorios A. Pavliotis & Petr Yatsyshin. (2019) Dynamics of the Desai-Zwanzig model in multiwell and random energy landscapes. Physical Review E 99:3.
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Piyush Grover, Kaivalya Bakshi & Evangelos A. Theodorou. (2018) A mean-field game model for homogeneous flocking. Chaos: An Interdisciplinary Journal of Nonlinear Science 28:6.
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Julian Tugaut. (2018) Convergence in Wasserstein distance for self-stabilizing diffusion evolving in a double-well landscape. Comptes Rendus Mathematique 356:6, pages 657-660.
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S. N. Gomes & G. A. Pavliotis. (2017) Mean Field Limits for Interacting Diffusions in a Two-Scale Potential. Journal of Nonlinear Science 28:3, pages 905-941.
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Manh Hong Duong & Julian Tugaut. (2018) The Vlasov-Fokker-Planck equation in non-convex landscapes: convergence to equilibrium. Electronic Communications in Probability 23:none.
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M.H. Duong & J. Tugaut. (2016) Stationary solutions of the Vlasov–Fokker–Planck equation: Existence, characterization and phase-transition. Applied Mathematics Letters 52, pages 38-45.
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Alethea B. T. Barbaro, José A. Can͂izo, José A. Carrillo & Pierre Degond. (2016) Phase Transitions in a Kinetic Flocking Model of Cucker--Smale Type. Multiscale Modeling & Simulation 14:3, pages 1063-1088.
Crossref

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