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arXiv · 1210.5865

Scaling limit for the random walk on the largest connected component of the critical random graph

David A. Croydon
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Abstract

A scaling limit for the simple random walk on the largest connected component of the Erdos-Renyi random graph in the critical window is deduced. The limiting diffusion is constructed using resistance form techniques, and is shown to satisfy the same quenched short-time heat kernel asymptotics as the Brownian motion on the continuum random tree.

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David A. Croydon. 2012-10-22. Scaling limit for the random walk on the largest connected component of the critical random graph. https://arxiv.org/abs/1210.5865

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