Concentration of measure for the number of isolated vertices in the Erdős-Rényi random graph by size bias couplings

DOI10.1016/j.spl.2011.06.002zbMath1226.05227arXiv1106.0048OpenAlexW2142748559MaRDI QIDQ643216

Subhankar Ghosh, Martin Raič, Larry Goldstein

Publication date: 28 October 2011

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.0048

zbMATH Keywords

large deviationssize biased couplingsgraph degree

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Random graphs (graph-theoretic aspects) (05C80) Combinatorial probability (60C05)

Related Items (4)

Central moment inequalities 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 ⋮ Weighted Poincaré inequalities, concentration inequalities and tail bounds related to Stein kernels in dimension one

Cites Work

• Applications of size biased couplings for concentration of measures
• Concentration of measures via size-biased couplings
• Normal approximation for coverage models over binomial point processes
• A central limit theorem for decomposable random variables with applications to random graphs
• Some large deviation results for sparse random graphs
• On the number of vertices of given degree in a random graph
• Poisson convergence and semi-induced properties of random graphs
• Poisson convergence and random graphs
• Multivariate normal approximations by Stein's method and size bias couplings
• CLT-related large deviation bounds based on Stein's method
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