Geometric ergodicity of Langevin dynamics with Coulomb interactions

DOI10.1088/1361-6544/ab514azbMath1427.82024arXiv1902.00602OpenAlexW2913426266MaRDI QIDQ5207514

Yulong Lu, Jonathan C. Mattingly

Publication date: 2 January 2020

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.00602

zbMATH Keywords

Lyapunov functionLangevin dynamicsgeometric ergodicityCoulomb gasinteracting particle system

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Interacting particle systems in time-dependent statistical mechanics (82C22) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Ergodicity, mixing, rates of mixing (37A25) Stochastic particle methods (65C35)

Related Items (14)

Random Batch Sum-of-Gaussians Method for Molecular Dynamics Simulations of Particle Systems ⋮ On explicit \(L^2\)-convergence rate estimate for underdamped Langevin dynamics ⋮ Recent advances in the long-time analysis of killed degenerate processes and their particle approximation ⋮ The Dyson and Coulomb games ⋮ On systems of particles in singular repulsive interaction in dimension one: log and Riesz gas ⋮ Exponential ergodicity for damping Hamiltonian dynamics with state-dependent and non-local collisions ⋮ Quasi-stationary distribution for Hamiltonian dynamics with singular potentials ⋮ PDMP characterisation of event-chain Monte Carlo algorithms for particle systems ⋮ Large deviations of empirical measures of diffusions in weighted topologies ⋮ Gamma calculus beyond Villani and explicit convergence estimates for Langevin dynamics with singular potentials ⋮ \(\mathrm{L}^2\)-hypocoercivity and large time asymptotics of the linearized Vlasov-Poisson-Fokker-Planck system ⋮ Coulomb Gases Under Constraint: Some Theoretical and Numerical Results ⋮ Convergence rates for the Vlasov-Fokker-Planck equation and uniform in time propagation of chaos in non convex cases ⋮ Weighted L ²-contractivity of Langevin dynamics with singular potentials

Cites Work

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• Mean field limit and propagation of chaos for Vlasov systems with bounded forces
• Construction, ergodicity and rate of convergence of \(N\)-particle Langevin dynamics with singular potentials
• Propagation of chaos for the 2D viscous vortex model
• 1D log gases and the renormalized energy: crystallization at vanishing temperature
• Large systems with Coulomb interactions: variational study and statistical mechanics
• A hypocoercivity related ergodicity method for singularly distorted non-symmetric diffusions
• Hypocoercivity for kinetic equations with linear relaxation terms
• Spectral properties of hypoelliptic operators
• Dynamics of a planar Coulomb gas
• Geometric ergodicity of two-dimensional Hamiltonian systems with a Lennard-Jones-like repulsive potential
• Simulating Coulomb and log-gases with hybrid Monte Carlo algorithms
• Fluctuations of two dimensional Coulomb gases
• Quantitative estimates of propagation of chaos for stochastic systems with \(W^{-1,\infty}\) kernels
• Large and moderate deviations and exponential convergence for stochastic damping Hamiltonian systems.
• 2D Coulomb gases and the renormalized energy
• Propagation of chaos for large Brownian particle system with Coulomb interaction
• Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing
• Hypoelliptic second order differential equations
• Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise.
• Higher-Dimensional Coulomb Gases and Renormalized Energy Functionals
• Partial Differential Equations for Probabilists
• Yet Another Look at Harris’ Ergodic Theorem for Markov Chains
• Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes
• Ergodicity and Lyapunov Functions for Langevin Dynamics with Singular Potentials
• Hypocoercivity for linear kinetic equations conserving mass
• Slow energy dissipation in anharmonic oscillator chains
• A Dynamical Approach to Random Matrix Theory
• Propagation of chaos for the Vlasov–Poisson–Fokker–Planck equation with a polynomial cut-off

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