Central limit theorem for the solution of the Kac equation

DOI10.1214/08-AAP524zbMath1161.82018arXiv0901.2464OpenAlexW3099086419MaRDI QIDQ2378633

Eugenio Regazzini, Ester Gabetta

Publication date: 13 January 2009

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0901.2464

zbMATH Keywords

rate of convergenceweak convergenceBoltzmann equationGaussian distributioncentral limit theoremnecessary and sufficient conditionsKac equationWild series

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Gas dynamics (general theory) (76N15) Kinetic theory of gases in time-dependent statistical mechanics (82C40)

Related Items (14)

Central limit theorems for solutions of the Kac equation: speed of approach to equilibrium in weak metrics ⋮ Central limit theorem in uniform metrics for generalized Kac equations ⋮ Explicit decay rate for the Gini index in the repeated averaging model ⋮ Kinetic models with randomly perturbed binary collisions ⋮ Multi-dimensional smoothing transformations: existence, regularity and stability of fixed points ⋮ Complete characterization of convergence to equilibrium for an inelastic Kac model ⋮ Proof of a McKean conjecture on the rate of convergence of Boltzmann-equation solutions ⋮ On the rate of explosion for infinite energy solutions of the spatially homogeneous Boltzmann equation ⋮ Probabilistic view of explosion in an inelastic Kac model ⋮ The role of the central limit theorem in discovering sharp rates of convergence to equilibrium for the solution of the Kac equation ⋮ Central limit theorem for a class of one-dimensional kinetic equations ⋮ Self-similar solutions of kinetic-type equations: the boundary case ⋮ Probabilistic study of the speed of approach to equilibrium for an inelastic Kac model ⋮ Characterization of weak convergence of probability-valued solutions of general one-dimensional kinetic equations

Cites Work

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• Speed of approach to equilibrium for Kac's caricature of a Maxwellian gas
• Asymptotic properties of the inelastic Kac model
• Some new results for McKean's graphs with applications to Kac's equation
• Exact solutions of the nonlinear Boltzmann equation and the theory of relaxation of a Maxwellian gas
• Fast and slow convergence to equilibrium for Maxwellian molecules via wild sums
• On the relation between rates of relaxation and convergence of wild sums for solutions of the Kac equation
• Bounds for Kac's master 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
• On the Depth of the Trees in the Mckean Representation of Wild's Sums
• An exponential formula for solving Boltzmann's equation for a Maxwellian gas

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