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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
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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 | ||||
|---|---|---|---|---|---|
| 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 | ||||
| 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| Status: | Not Peer Reviewed | ||||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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