Complete characterization of convergence to equilibrium for an inelastic Kac model

DOI10.1007/S10955-012-0505-YzbMath1254.82034arXiv1202.3633OpenAlexW3098168371MaRDI QIDQ438836

Ester Gabetta, Eugenio Regazzini

Publication date: 31 July 2012

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

Full work available at URL: https://arxiv.org/abs/1202.3633

zbMATH Keywords

Cauchy problemdistribution functionstable lawstationary solutionconvergence to equilibriumBoltzmann-like equationinelastic Kac equationMaxwellian gasstandard domain of attraction

Mathematics Subject Classification ID

Kinetic theory of gases in time-dependent statistical mechanics (82C40) Kinetic theory of gases in equilibrium statistical mechanics (82B40) Singular nonlinear integral equations (45G05)

Related Items (3)

Local stability of perfect alignment for a spatially homogeneous kinetic model ⋮ Probabilistic view of explosion in an inelastic Kac model ⋮ Characterization of weak convergence of probability-valued solutions of general one-dimensional kinetic equations

Cites Work

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• Proof of a McKean conjecture on the rate of convergence of Boltzmann-equation solutions
• Speed of approach to equilibrium for Kac's caricature of a Maxwellian gas
• Self-similar solutions in one-dimensional kinetic models: a probabilistic view
• Asymptotic properties of the inelastic Kac model
• Central limit theorem for a class of one-dimensional kinetic equations
• Central limit theorems for solutions of the Kac equation: speed of approach to equilibrium in weak metrics
• Mathematics of granular materials
• Some new results for McKean's graphs with applications to Kac's equation
• The role of the central limit theorem in discovering sharp rates of convergence to equilibrium for the solution of the Kac equation
• Reaching the best possible rate of convergence to equilibrium for solutions of Kac's equation via central limit theorem
• Probabilistic study of the speed of approach to equilibrium for an inelastic Kac model
• On the self-similar asymptotics for generalized nonlinear kinetic Maxwell models
• Fixed points of the smoothing transform: two-sided solutions
• Central limit theorem for the solution of the Kac equation
• On the rate of explosion for infinite energy solutions of the spatially homogeneous Boltzmann equation
• A Central Limit Problem for Partially ExchangeableRandom Variables
• Central limit theorem for Maxwellian molecules and truncation of the wild expansion
• Real Analysis and Probability
• Probabilistic Investigations on the Explosion of Solutions of the KAC Equation with Infinite Energy Initial Distribution
• An exponential formula for solving Boltzmann's equation for a Maxwellian gas

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