Asymptotic for the cumulative distribution function of the degrees and homomorphism densities for random graphs sampled from a graphon

2018/07/26 by Jean‐François Delmas, Jean-François Delmas, Jean‐Stéphane Dhersin +5 · 1 citation
Decision Sciences · Mathematics · #Probability and Risk Models #Statistical Methods and Inference #Stochastic processes and statistical mechanics #math.PR #msc:05C07 #msc:05C80 #msc:60C05 #msc:60F05 #msc:60G57

paper · pdf · doi:10.48550/arxiv.1807.09989

49 pages, 3 figures

arxiv created 2018/07/26 · arxiv updated 2018/07/27

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.

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• Asymptotic Normality of Subgraph Counts in Sparse Inhomogeneous Random Graphs

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