The role of the central limit theorem in discovering sharp rates of convergence to equilibrium for the solution of the Kac equation

DOI10.1214/09-AAP623zbMath1195.60033arXiv1009.3406MaRDI QIDQ968772

Eugenio Regazzini, Emanuele Dolera

Publication date: 6 May 2010

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

Full work available at URL: https://arxiv.org/abs/1009.3406

zbMATH Keywords

cumulantscentral limit theoremtotal variation distanceBerry-Esseen inequalitieskurtosis coefficientWild's sum

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Kinetic theory of gases in time-dependent statistical mechanics (82C40)

Related Items (12)

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 ⋮ Multi-dimensional smoothing transformations: existence, regularity and stability of fixed points ⋮ Complete characterization of convergence to equilibrium for an inelastic Kac model ⋮ Estimates of the approximation of weighted sums of conditionally independent random variables by the normal law ⋮ Proof of a McKean conjecture on the rate of convergence of Boltzmann-equation solutions ⋮ Probabilistic view of explosion in an inelastic Kac model ⋮ Asymptotic of grazing collisions and particle approximation for the Kac equation without Cutoff ⋮ Central limit theorem for a class of one-dimensional kinetic equations ⋮ Rates of convergence in de Finetti's representation theorem, and Hausdorff moment problem ⋮ 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
• Central limit theorems for solutions of the Kac equation: speed of approach to equilibrium in weak metrics
• Some new results for McKean's graphs with applications to Kac's equation
• Reaching the best possible rate of convergence to equilibrium for solutions of Kac's equation via central limit theorem
• 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
• Central limit theorem for the solution of the Kac equation
• Toeplitz matrices, translation kernels and a related problem in probability theory
• Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law

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