Upper bounds for the largest components in critical inhomogeneous random graphs

Umberto De Ambroggio; Angelica Pachon

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arXiv · 2012.09001

Upper bounds for the largest components in critical inhomogeneous random graphs

Umberto De Ambroggio·Angelica Pachon

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Abstract

We consider the Norros-Reittu random graph $NR_n(\textbf{w})$, where edges are present independently but edge probabilities are moderated by vertex weights, and use probabilistic arguments based on martingales to analyse the component sizes in this model when considered at criticality. In particular, we obtain stronger upper bounds (with respect to those available in the literature) for the probability of observing unusually large maximal clusters, and simplify the arguments needed to derive polynomial upper bounds for the probability of observing unusually small largest components.

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Umberto De Ambroggio, Angelica Pachon. 2020-12-16. Upper bounds for the largest components in critical inhomogeneous random graphs. https://arxiv.org/abs/2012.09001

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