Some new results for McKean's graphs with applications to Kac's equation

DOI10.1007/s10955-006-9187-7zbMath1107.82046OpenAlexW2044417169MaRDI QIDQ867698

Eugenio Regazzini, Ester Gabetta

Publication date: 16 February 2007

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

Full work available at URL: https://doi.org/10.1007/s10955-006-9187-7

zbMATH Keywords

depth of a leafdepth of a treeKac's equationMcKean binary tree (or graph)rate of convergence of Wild sumsStirling numbers (of the first kind)Wild convolutionWild sum

Mathematics Subject Classification ID

Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Kinetic theory of gases in time-dependent statistical mechanics (82C40)

Related Items (15)

Central limit theorem for the solution of the Kac equation ⋮ Central limit theorems for solutions of the Kac equation: speed of approach to equilibrium in weak metrics ⋮ 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 ⋮ On the Depth of the Trees in the Mckean Representation of Wild's Sums ⋮ Central limit theorem for a class of one-dimensional kinetic equations ⋮ A conversation with Eugenio Regazzini ⋮ Self-similar solutions of kinetic-type equations: the boundary case ⋮ Probabilistic Investigations on the Explosion of Solutions of the KAC Equation with Infinite Energy Initial Distribution ⋮ 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 ⋮ Characterization of weak convergence of probability-valued solutions of general one-dimensional kinetic equations

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