A Survey on the Lace Expansion for the Nearest-neighbor Models on the BCC Lattice

被引：3
|
作者：
Handa, Satoshi [1 ,2 ]
Kamijima, Yoshinori [1 ]
Sakai, Akira [3 ]
机构：
[1] Hokkaido Univ, Grad Sch Sci, Dept Math, Sapporo, Hokkaido, Japan
[2] Fujitsu Labs Ltd, Kawasaki, Kanagawa, Japan
[3] Hokkaido Univ, Fac Sci, Sapporo, Hokkaido, Japan
来源：
TAIWANESE JOURNAL OF MATHEMATICS | 2020年 / 24卷 / 03期
关键词：
self-avoiding walk; percolation; mean-field behavior; upper critical dimension; lace expansion; FIELD CRITICAL-BEHAVIOR; SELF-AVOIDING WALK; PHASE-TRANSITION; PERCOLATION; SHARPNESS;
D O I：
10.11650/tjm/190904
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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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页码：723 / 784
页数：62
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