Loop Correlations in Random Wire Models

Costanza Benassi, Daniel Ueltschi

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
11 Downloads (Pure)

Abstract

We introduce a family of loop soup models on the hypercubic lattice. The models involve links on the edges, and random pairings of the link endpoints on the sites. We conjecture that loop correlations of distant points are given by Poisson-Dirichlet correlations in dimensions three and higher. We prove that, in a specific random wire model that is related to the classical XY spin system, the probability that distant sites form an even partition is given by the Poisson-Dirichlet counterpart.
Original languageEnglish
Pages (from-to)525-547
Number of pages23
JournalCommunications in Mathematical Physics
Volume374
Issue number2
Early online date8 Jun 2019
DOIs
Publication statusPublished - Mar 2020

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