On the fluctuations about the Vlasov limit for \(N\)-particle systems with mean-field interactions

DOI10.1007/s10955-009-9800-7zbMath1185.82056OpenAlexW2136402916MaRDI QIDQ1035821

Carlo Lancellotti

Publication date: 4 November 2009

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10955-009-9800-7

zbMATH Keywords

central limit theoremsVlasov equationmean-field limitfluctuation dynamicsSznitman-Tanaka theorem

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Statistical mechanics of plasmas (82D10) Vlasov equations (35Q83)

Related Items (12)

The two-particle correlation function for systems with long-range interactions ⋮ Time-asymptotic evolution of spatially uniform Gaussian Vlasov fluctuation fields ⋮ On the Glassey-Schaeffer Estimates for Linear Landau Damping ⋮ On the size of chaos via Glauber calculus in the classical mean-field dynamics ⋮ Bulk Topological States in a New Collective Dynamics Model ⋮ Gaussian fluctuations for interacting particle systems with singular kernels ⋮ Microscopic foundations of kinetic plasma theory: the relativistic Vlasov-Maxwell equations and their radiation-reaction-corrected generalization ⋮ Classical Heisenberg spins with long-range interactions: relaxation to equilibrium for finite systems ⋮ Interacting particle systems with long-range interactions: scaling limits and kinetic equations ⋮ Mean-Field Limit of a Microscopic Individual-Based Model Describing Collective Motions ⋮ Dynamical large deviations for homogeneous systems with long range interactions and the Balescu-Guernsey-Lenard equation ⋮ A review of the mean field limits for Vlasov equations

Cites Work

• Second derivatives of convex functions in the sense of A.\ D.\ Aleksandrov on infinite-dimensional spaces with measure
• The Vlasov dynamics and its fluctuations in the \(1/N\) limit of interacting classical particles
• Vlasov equations
• A Hilbertian approach for fluctuations on the McKean-Vlasov model
• Microscopic derivations of Vlasov equations
• The Vlasov limit for a system of particles which interact with a wave field
• A Topological Version of Slutsky's Theorem
• Foundations of Modern Probability
• Real Analysis and Probability
• A CLASS OF MARKOV PROCESSES ASSOCIATED WITH NONLINEAR PARABOLIC EQUATIONS
• Bounded Measures on Topological Spaces
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