Conditioned Poisson distributions and the concentration of chromatic numbers
Discrete Mathematics
2011-07-20 v1 Statistics Theory
Statistics Theory
Abstract
The paper provides a simpler method for proving a delicate inequality that was used by Achlioptis and Naor to establish asymptotic concentration for chromatic numbers of Erdos-Renyi random graphs. The simplifications come from two new ideas. The first involves a sharpened form of a piece of statistical folklore regarding goodness-of-fit tests for two-way tables of Poisson counts under linear conditioning constraints. The second idea takes the form of a new inequality that controls the extreme tails of the distribution of a quadratic form in independent Poissons random variables.
Keywords
Cite
@article{arxiv.1107.3818,
title = {Conditioned Poisson distributions and the concentration of chromatic numbers},
author = {John Hartigan and David Pollard and Sekhar Tatikonda},
journal= {arXiv preprint arXiv:1107.3818},
year = {2011}
}
Comments
Unpublished paper from June 2008