Loop Correlations in Random Wire Models

Costanza Benassi; Daniel Ueltschi

doi:10.1007/s00220-019-03474-9

Loop Correlations in Random Wire Models

Costanza Benassi, Daniel Ueltschi

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

98 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 language	English
Pages (from-to)	525-547
Number of pages	23
Journal	Communications in Mathematical Physics
Volume	374
Issue number	2
Early online date	8 Jun 2019
DOIs	https://doi.org/10.1007/s00220-019-03474-9
Publication status	Published - 8 Mar 2020

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random_wiresAccepted author manuscript, 483 KB
Benassi-Ueltschi2019_Article_LoopCorrelationsInRandomWireMoFinal published version, 557 KBLicence: CC BY
Benassi-Ueltschi2020_Article_LoopCorrelationsInRandomWireMoFinal published version, 547 KBLicence: CC BY

Cite this

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title = "Loop Correlations in Random Wire Models",

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. ",

author = "Costanza Benassi and Daniel Ueltschi",

note = "Funding Information: We are grateful to Jakob Bj?rnberg, J?rg Fr?hlich, Peter M?rters, Charles-?douard Pfister, Vedran Sohinger, Akinori Tanaka, and Yvan Velenik, for useful discussions. We thank the referee for valuable comments. CB is supported by the Leverhulme Trust Research Project Grant RPG-2017-228. Publisher Copyright: {\textcopyright} 2019, The Author(s).",

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T1 - Loop Correlations in Random Wire Models

AU - Benassi, Costanza

AU - Ueltschi, Daniel

N1 - Funding Information: We are grateful to Jakob Bj?rnberg, J?rg Fr?hlich, Peter M?rters, Charles-?douard Pfister, Vedran Sohinger, Akinori Tanaka, and Yvan Velenik, for useful discussions. We thank the referee for valuable comments. CB is supported by the Leverhulme Trust Research Project Grant RPG-2017-228. Publisher Copyright: © 2019, The Author(s).

PY - 2020/3/8

Y1 - 2020/3/8

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/85067300845

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DO - 10.1007/s00220-019-03474-9

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SN - 0010-3616

VL - 374

SP - 525

EP - 547

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 2

ER -

Loop Correlations in Random Wire Models

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