Croydon, David A.. (2011) Scaling limit for the random walk on the largest connected component of the critical random graph. Research Institute for Mathematical Sciences. Publications, Vol.48 (No.2). pp. 279-338. ISSN 1663-4926

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Abstract

In this article, a scaling limit for the simple random walk on the largest connected component of the Erdos-Rényi random graph G(n,p) in the critical window, p = n−1+λn−4/3, 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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Random walks (Mathematics)
Journal or Publication Title:	Research Institute for Mathematical Sciences. Publications
Publisher:	European Mathematical Society Publishing House
ISSN:	1663-4926
Date:	November 2011
Volume:	Vol.48
Number:	No.2
Page Range:	pp. 279-338
Identification Number:	10.2977/PRIMS/70
Status:	Not Peer Reviewed
Publication Status:	Published
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URI:	http://wrap.warwick.ac.uk/id/eprint/39469

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