A survey on the lace expansion for the nearest-neighbor models on the BCC lattice

Satoshi Handa; Yoshinori Kamijima; Akira Sakai

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arXiv · 1712.05573

A survey on the lace expansion for the nearest-neighbor models on the BCC lattice

Satoshi Handa·Yoshinori Kamijima·Akira Sakai

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Abstract

The aim of this survey is to explain, in a self-contained and relatively beginner-friendly manner, the lace expansion for the nearest-neighbor models of self-avoiding walk and percolation that converges in all dimensions above 6 and 9, respectively. To achieve this, we consider a $d$-dimensional version of the body-centered cubic (BCC) lattice, on which it is extremely easy to enumerate various random-walk quantities. Also, we choose a particular set of bootstrapping functions, by which a notoriously complicated part of the lace-expansion analysis becomes rather transparent.

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Satoshi Handa, Yoshinori Kamijima, Akira Sakai. 2017-12-15. A survey on the lace expansion for the nearest-neighbor models on the BCC lattice. https://arxiv.org/abs/1712.05573

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