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

David A. Croydon | Zendy

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

Author(s) -

David A. Croydon

Publication year - 2012

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/70

Subject(s) - mathematics , random walk , scaling limit , scaling , random graph , connected component , limit (mathematics) , component (thermodynamics) , statistical physics , heterogeneous random walk in one dimension , graph , combinatorics , discrete mathematics , statistics , mathematical analysis , physics , quantum mechanics , geometry

In this article, a scaling limit for the simple random walk on the largest connected component of the Erdos-Renyi 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.

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