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2021 Sharp phase transition for random loop models on trees
Volker Betz, Johannes Ehlert, Benjamin Lees, Lukas Roth
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Electron. J. Probab. 26: 1-26 (2021). DOI: 10.1214/21-EJP677


We investigate the random loop model on the d-ary tree. For d3, 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 d1. The corresponding coefficients can be determined in a schematic way and we calculate them up to order 6.

Funding Statement

The research of BL was supported by the Alexander von Humboldt Foundation.


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Volker Betz. Johannes Ehlert. Benjamin Lees. Lukas Roth. "Sharp phase transition for random loop models on trees." Electron. J. Probab. 26 1 - 26, 2021.


Received: 25 September 2020; Accepted: 7 July 2021; Published: 2021
First available in Project Euclid: 25 November 2021

Digital Object Identifier: 10.1214/21-EJP677

Primary: 60

Keywords: phase transition , random interchange , Random loop model , Random Stirring


Vol.26 • 2021
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