Self-similar solutions in one-dimensional kinetic models: a probabilistic view

DOI10.1214/11-AAP818zbMath1259.82087arXiv1003.5527OpenAlexW3098986064MaRDI QIDQ691109

Federico Bassetti, Lucia Ladelli

Publication date: 29 November 2012

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

Full work available at URL: https://arxiv.org/abs/1003.5527

zbMATH Keywords

self-similar solutioncentral limit theoremstable lawKac modeldomain of normal attractionmarked recursive \(N\)-ary random treessmoothing transformations

Mathematics Subject Classification ID

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

Related Items (16)

Solutions to complex smoothing equations ⋮ On multidimensional Mandelbrot cascades ⋮ 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 ⋮ Solutions of kinetic-type equations with perturbed collisions ⋮ Heavy tailed solutions of multivariate smoothing transforms ⋮ Proof of a McKean conjecture on the rate of convergence of Boltzmann-equation solutions ⋮ Probabilistic view of explosion in an inelastic Kac model ⋮ Self-similar solutions of kinetic-type equations: the boundary case ⋮ Self-similar solutions to kinetic-type evolution equations: beyond the boundary case ⋮ Precise tail asymptotics of fixed points of the smoothing transform with general weights ⋮ Mean field dynamics of interaction processes with duplication, loss and copy ⋮ Characterization of weak convergence of probability-valued solutions of general one-dimensional kinetic equations

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