The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Publications of the Research Institute for Mathematical Sciences


Full-Text PDF (677 KB) | Metadata | Table of Contents | PRIMS summary
Volume 48, Issue 2, 2012, pp. 279–338
DOI: 10.2977/PRIMS/70

Published online: 2012-06-03

Scaling Limit for the Random Walk on the Largest Connected Component of the Critical Random Graph

David A. Croydon[1]

(1) Warwick University, Coventry, UK

A scaling limit for the simple random walk on the largest connected component of the Erd\H{o}s-R\'{e}nyi random graph $G(n,p)$ in the critical window, $p=n^{-1}+\lambda n^{-4/3}$, 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.

Keywords: random graphs, random walk in random environment, scaling limit, continuum random tree

Croydon David: Scaling Limit for the Random Walk on the Largest Connected Component of the Critical Random Graph. Publ. Res. Inst. Math. Sci. 48 (2012), 279-338. doi: 10.2977/PRIMS/70