Sharp phase transition for random loop models on trees

被引：0

作者：

Betz, Volker ^{[1
]}

Ehlert, Johannes ^{[1
]}

Lees, Benjamin ^{[2
]}

Roth, Lukas ^{[1
]}

机构：

[1] Tech Univ Darmstadt, Darmstadt, Germany

[2] Univ Bristol, Bristol, Avon, England

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2021年 / 26卷

关键词：

random loop model; random interchange; random stirring; phase transition; INFINITE CYCLES;

D O I：

10.1214/21-EJP677

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We investigate the random loop model on the d-ary tree. For d >= 3, we establish a (locally) sharp phase transition for the existence of infinite loops. Moreover, we derive rigorous bounds that in principle allow to determine the value of the critical parameter with arbitrary precision. Additionally, we prove the existence of an asymptotic expansion for the critical parameter in terms of d-1. The corresponding coefficients can be determined in a schematic way and we calculate them up to order 6.

引用

页数：26

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