Corpus ID: 119685833

# Large deviation for the empirical degree distribution of an Erdos-Renyi graph

@article{Mukherjee2013LargeDF,
title={Large deviation for the empirical degree distribution of an Erdos-Renyi graph},
author={S. Mukherjee},
journal={arXiv: Probability},
year={2013}
}
With $(d_1,\cdots,d_n)$ denoting the labeled degrees of an Erdos Renyi graph with parameter $\beta/n$, the large deviation principle for $\frac{1}{n}\sum\limits_{j=1}^n\delta_{d_j}$ (the empirical distribution of the degrees) is derived with a good rate function, with respect to a topology stronger than the weak topology. As an application the degeneracy of some sparse ERGM models used in social networks is studied rigorously, showing in particular that using terms such as "gwd (geometrically… Expand

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