Asymptotic for the cumulative distribution function of the degrees and homomorphism densities for random graphs sampled from a graphon
Probability
2018-07-27 v1
Abstract
We give asymptotics for the cumulative distribution function (CDF) for degrees of large dense random graphs sampled from a graphon. The proof is based on precise asymptotics for binomial random variables. Replacing the indicator function in the empirical CDF by a smoother function, we get general asymptotic results for functionals of homomorphism densities for partially labeled graphs with smoother functions. This general setting allows to recover recent results on asymptotics for homomorphism densities of sampled graphon.
Keywords
Cite
@article{arxiv.1807.09989,
title = {Asymptotic for the cumulative distribution function of the degrees and homomorphism densities for random graphs sampled from a graphon},
author = {Jean-François Delmas and Jean-Stéphane Dhersin and Marion Sciauveau},
journal= {arXiv preprint arXiv:1807.09989},
year = {2018}
}
Comments
49 pages, 3 figures