On the Depth of the Trees in the Mckean Representation of Wild's Sums

DOI10.1080/00411450701468217zbMath1183.82053OpenAlexW2005567933MaRDI QIDQ5429688

Federico Bassetti, Ester Gabetta, Eugenio Regazzini

Publication date: 3 December 2007

Published in: Transport Theory and Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00411450701468217

zbMATH Keywords

gamma distributionKac equationWild convolutionmultiple hypergeometric functiondepth of a McKean tree (probability distribution of)McKean treewild sum

Mathematics Subject Classification ID

Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics (82C41)

Related Items (3)

Central limit theorem for the solution of the Kac equation ⋮ 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

Cites Work

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• Speed of approach to equilibrium for Kac's caricature of a Maxwellian gas
• Some new results for McKean's graphs with applications to Kac's equation
• On the relation between rates of relaxation and convergence of wild sums for solutions of the Kac equation
• Lauricella's hypergeometric function \(F_ D\)
• The height of a random binary search tree
• Central limit theorem for Maxwellian molecules and truncation of the wild expansion
• An exponential formula for solving Boltzmann's equation for a Maxwellian gas

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