Dynamics of a planar Coulomb gas

DOI10.1214/18-AAP1386zbMath1401.82022arXiv1706.08776OpenAlexW2726822844MaRDI QIDQ1617160

Djalil Chafaï, François Bolley, Joaquin Fontbona

Publication date: 7 November 2018

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.08776

zbMATH Keywords

Lyapunov functionPoincaré inequalityCoulomb gasinteracting particle systemGinibre ensembleMcKean-Vlasov equationCox-Ingersoll-Ross processMarkov diffusion process

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Interacting particle systems in time-dependent statistical mechanics (82C22) Brownian motion (60J65) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Random matrices (algebraic aspects) (15B52) Stochastic particle methods (65C35) Vlasov equations (35Q83)

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Cites Work

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• Around the circular law
• Propagation of chaos for the 2D viscous vortex model
• First-order global asymptotics for confined particles with singular pair repulsion
• Hitting times, functional inequalities, Lyapunov conditions and uniform ergodicity
• Lyapunov conditions for super Poincaré inequalities
• A simple proof of the Poincaré inequality for a large class of probability measures
• Block diagonally dominant matrices and generalizations of the Gerschgorin circle theorem
• A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description
• A nonlinear stochastic differential equation involving the Hilbert transform
• Interacting Brownian particles and the Wigner law
• Diffusing particles with electrostatic repulsion
• Isoperimetric and analytic inequalities for log-concave probability measures
• Stochastic particle approximation of the Keller-Segel equation and two-dimensional generalization of Bessel processes
• Logarithmic Sobolev inequalities for some nonlinear PDE's.
• Large deviations upper bounds for the laws of matrix-valued processes and non-commutative entropies
• A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description. II
• Paths clustering and an existence result for stochastic vortex systems
• Uniqueness for a weak nonlinear evolution equation and large deviations for diffusing particles with electrostatic repulsion
• A Theory of the Term Structure of Interest Rates
• Non-Hermitian Random Matrix Ensembles
• Ornstein–Uhlenbeck diffusion of hermitian and non-hermitian matrices—unexpected links
• An Introduction to Random Matrices
• Analysis and Geometry of Markov Diffusion Operators
• On the long time behavior of stochastic vortices systems
• Statistical Ensembles of Complex, Quaternion, and Real Matrices
• A Dynamical Approach to Random Matrix Theory
• The 2-D stochastic Keller-Segel particle model : existence and uniqueness
• Mean-Field Limits for Some Riesz Interaction Gradient Flows
• Spectral gap for spherically symmetric \(\log\)-concave probability measures, and beyond