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Search: MSC category 82B41 ( Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41] )

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1. CJM 2004 (vol 56 pp. 77)

Holmes, Mark; Járai, Antal A.; Sakai, Akira; Slade, Gordon
High-Dimensional Graphical Networks of Self-Avoiding Walks
We use the lace expansion to analyse networks of mutually-avoiding self-avoiding walks, having the topology of a graph. The networks are defined in terms of spread-out self-avoiding walks that are permitted to take large steps. We study the asymptotic behaviour of networks in the limit of widely separated network branch points, and prove Gaussian behaviour for sufficiently spread-out networks on $\mathbb{Z}^d$ in dimensions $d>4$.

Categories:82B41, 60K35

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