Loop correlations in random wire models
| Autor: | Costanza Benassi, Daniel Ueltschi |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
G100
Conjecture F300 010102 general mathematics Probability (math.PR) Complex system Spin system FOS: Physical sciences Statistical and Nonlinear Physics 60C05 60K35 82B05 82B20 82B26 Mathematical Physics (math-ph) 01 natural sciences Lattice (order) 0103 physical sciences FOS: Mathematics Partition (number theory) 010307 mathematical physics Statistical physics 0101 mathematics Mathematics - Probability Mathematical Physics Mathematics |
| ISSN: | 0010-3616 |
| DOI: | 10.48550/arxiv.1807.06564 |
| Popis: | 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. Comment: 20 pages, 5 figures. An error in Prop. 4.1 has been corrected |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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