Bounded size bias coupling: a gamma function bound, and universal Dickman-function behavior

DOI10.1007/s00440-014-0572-xzbMath1323.60034arXiv1306.0157OpenAlexW2082241645MaRDI QIDQ495548

Richard Arratia, Peter H. Baxendale

Publication date: 14 September 2015

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.0157

zbMATH Keywords

couplingconcentration inequalitiessize biasChernoff-Hoeffding boundsDickman function

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15)

Related Items (13)

Relaxation of monotone coupling conditions: Poisson approximation and beyond ⋮ Concentration inequalities from monotone couplings for graphs, walks, trees and branching processes ⋮ On the largest part size of low‐rank combinatorial assemblies ⋮ Negative dependence and stochastic orderings ⋮ Concentration inequalities using approximate zero bias couplings with applications to Hoeffding’s statistic under the Ewens distribution ⋮ Particle density in diffusion-limited annihilating systems ⋮ Central moment inequalities using Stein's method ⋮ Error bounds in local limit theorems using Stein's method ⋮ Size biased couplings and the spectral gap for random regular graphs ⋮ Bounded size biased couplings, log concave distributions and concentration of measure for occupancy models ⋮ Size bias for one and all ⋮ Asymptotic distribution for the birthday problem with multiple coincidences, via an embedding of the collision process ⋮ A generalised Dickman distribution and the number of species in a negative binomial process model

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