Uniqueness thresholds on trees versus graphs

Allan Sly

doi:10.1214/07-AAP508

Uniqueness thresholds on trees versus graphs

Allan Sly

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

7 Scopus citations

Abstract

Counter to the general notion that the regular tree is the worst case for decay of correlation between sets and nodes, we produce an example of a multi-spin interacting system which has uniqueness on the d-regular tree but does not have uniqueness on some infinite d-regular graphs.

Original language	English (US)
Pages (from-to)	1897-1909
Number of pages	13
Journal	Annals of Applied Probability
Volume	18
Issue number	5
DOIs	https://doi.org/10.1214/07-AAP508
State	Published - Oct 2008
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Potts model
Uniqueness

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10.1214/07-AAP508

Cite this

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title = "Uniqueness thresholds on trees versus graphs",

abstract = "Counter to the general notion that the regular tree is the worst case for decay of correlation between sets and nodes, we produce an example of a multi-spin interacting system which has uniqueness on the d-regular tree but does not have uniqueness on some infinite d-regular graphs.",

keywords = "Potts model, Uniqueness",

author = "Allan Sly",

year = "2008",

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doi = "10.1214/07-AAP508",

language = "English (US)",

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pages = "1897--1909",

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AU - Sly, Allan

PY - 2008/10

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N2 - Counter to the general notion that the regular tree is the worst case for decay of correlation between sets and nodes, we produce an example of a multi-spin interacting system which has uniqueness on the d-regular tree but does not have uniqueness on some infinite d-regular graphs.

AB - Counter to the general notion that the regular tree is the worst case for decay of correlation between sets and nodes, we produce an example of a multi-spin interacting system which has uniqueness on the d-regular tree but does not have uniqueness on some infinite d-regular graphs.

KW - Potts model

KW - Uniqueness

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DO - 10.1214/07-AAP508

M3 - Article

AN - SCOPUS:63049112024

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SP - 1897

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JO - Annals of Applied Probability

JF - Annals of Applied Probability

IS - 5

ER -

Uniqueness thresholds on trees versus graphs

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

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