Brownian particles with electrostatic repulsion on the circle: Dyson's model for unitary random matrices revisited

DOI10.1051/ps:2001109zbMath1002.60093OpenAlexW2133130261MaRDI QIDQ4534850

Emmanuel Cépa, Dominique Lépingle

Publication date: 11 June 2002

Published in: ESAIM: Probability and Statistics (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=PS_2001__5__203_0

zbMATH Keywords

repulsive particlesdeterministic second-order partial differential equations

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Brownian motion (60J65) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Stochastic methods applied to problems in equilibrium statistical mechanics (82B31)

Related Items (19)

Nonlinear martingale problems involving singular integrals ⋮ Averaging principle for stochastic variational inequalities with application to PDEs with nonlinear Neumann conditions ⋮ Functional equations solving initial-value problems of complex Burgers-type equations for one-dimensional log-gases ⋮ The Heckman-Opdam Markov processes ⋮ Strong solutions to a beta-Wishart particle system ⋮ Local law and rigidity for unitary Brownian motion ⋮ Determinantal martingales and noncolliding diffusion processes ⋮ The Dyson and Coulomb games ⋮ Optimal cooperative searching using purely repulsive interactions ⋮ Malliavin calculus for non-colliding particle systems ⋮ Tightness results for infinite-slit limits of the chordal Loewner equation ⋮ Spiking the random matrix hard edge ⋮ Towards a characterization of Markov processes enjoying the time-inversion property ⋮ Uniqueness for a weak nonlinear evolution equation and large deviations for diffusing particles with electrostatic repulsion ⋮ Strong solutions of stochastic equations with singular time dependent drift ⋮ β-Jacobi processes ⋮ Some properties of the Wishart processes and a matrix extension of the Hartman-Watson laws ⋮ Limits of radial multiple SLE and a Burgers-Loewner differential equation ⋮ Radial Dunkl processes: existence, uniqueness and hitting time

Cites Work

• On the convergence of diffusion processes conditioned to remain in a bounded region for large time to limiting positive recurrent diffusion processes
• Stochastic differential equations for multi-dimensional domain with reflecting boundary
• Stochastic differential equations with reflecting boundary condition in convex regions
• The Wigner semi-circle law and eigenvalues of matrix-valued diffusions
• Brownian motion in a Weyl chamber, non-colliding particles, and random matrices
• A nonlinear stochastic differential equation involving the Hilbert transform
• Multivalued Skorohod problem
• Interacting Brownian particles and the Wigner law
• Diffusing particles with electrostatic repulsion
• A diffusion process in a singular mean-drift-field
• Stochastic differential equations with reflecting boundary conditions
• A Brownian-Motion Model for the Eigenvalues of a Random Matrix
• Non‐Colliding Brownian Motions on the Circle
• Diffusion Processes in One Dimension
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