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Scaling limit for the random walk on the largest connected component of the critical random graph
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Croydon, David A. (2012) 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. doi:10.2977/PRIMS/70 ISSN 1663-4926.
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Official URL: http://dx.doi.org/10.2977/PRIMS/70
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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > 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 | ||||
Official Date: | 2012 | ||||
Dates: |
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Volume: | Vol.48 | ||||
Number: | No.2 | ||||
Page Range: | pp. 279-338 | ||||
DOI: | 10.2977/PRIMS/70 | ||||
Status: | Not Peer Reviewed | ||||
Publication Status: | Published |
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