Local Limit Theorems for Sequences of Simple Random Walks on Graphs |
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Authors: | D. A. Croydon B. M. Hambly |
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Affiliation: | (1) Department of Statistics, University of Warwick, Coventry, CV4 7AL, UK;(2) Mathematical Institute, 24-29 St. Giles’, Oxford, OX1 3LB, UK |
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Abstract: | In this article, local limit theorems for sequences of simple random walks on graphs are established. The results formulated are motivated by a variety of random graph models, and explanations are provided as to how they apply to supercritical percolation clusters, graph trees converging to the continuum random tree and the homogenisation problem for nested fractals. A subsequential local limit theorem for the simple random walks on generalised Sierpinski carpet graphs is also presented. |
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Keywords: | Local limit theorem Random walk Parabolic Harnack inequality Resistance metric |
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