Diffusion approximation for Fokker Planck with heavy tail equilibria: a spectral method in dimension 1

DOI10.1007/s00220-019-03315-9zbMath1422.60144arXiv1711.03060OpenAlexW2964318562MaRDI QIDQ1731123

Marjolaine Puel, Gilles Lebeau

Publication date: 20 March 2019

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.03060

zbMATH Keywords

Fokker Planckheavy tail equilibria

Mathematics Subject Classification ID

Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70) Fokker-Planck equations (35Q84)

Related Items (8)

Fractional diffusion for Fokker–Planck equation with heavy tail equilibrium: An à la Koch spectral method in any dimension ⋮ Stable limit theorems for additive functionals of one-dimensional diffusion processes ⋮ Quantitative fluid approximation in transport theory: a unified approach ⋮ Anomalous diffusion for multi-dimensional critical kinetic Fokker-Planck equations ⋮ One dimensional critical kinetic Fokker-Planck equations, Bessel and stable processes ⋮ Classical and quantum mechanical models of many-particle systems. Abstracts from the workshop held November 29 -- December 5, 2020 (online meeting) ⋮ Fractional Fokker--Planck Equation with General Confinement Force ⋮ Fractional hypocoercivity

Cites Work

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• Fractional diffusion limit for collisional kinetic equations: a Hilbert expansion approach
• Anomalous transport of particles in plasma physics
• Fractional diffusion limit for collisional kinetic equations
• Functional inequalities for heavy tailed distributions and application to isoperimetry
• A simple proof of the Poincaré inequality for a large class of probability measures
• Boundary layers and homogenization of transport processes
• Diffusion limit for kinetic Fokker-Planck equation with heavy tails equilibria: the critical case
• ANOMALOUS DIFFUSION LIMIT FOR KINETIC EQUATIONS WITH DEGENERATE COLLISION FREQUENCY
• Fractional diffusion limit for collisional kinetic equations: A moments method
• Global existence of smooth solutions for the Vlasov-Fokker-Planck equation in $1$ and $2$ space dimensions
• Existence of solutions and diffusion approximation for a model Fokker-Planck equation
• Diffusion limit of Fokker−Planck equation with heavy tail equilibria
• Weak Poincaré inequalities and \(L^2\)-convergence rates of Markov semigroups

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