Correlation inequalities for edge-reinforced random walk

Franz Merkl; Silke W.W. Rolles

doi:10.1214/ECP.v16-1683

Correlation inequalities for edge-reinforced random walk

Franz Merkl, Silke W.W. Rolles

Associate Professorship of Probability Theory

University of Munich

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

1 Scopus citations

Abstract

We prove correlation inequalities for linearly edge-reinforced random walk. These correlation inequalities concern the first entry tree, i.e. the tree of edges used to enter any vertex for the first time. They also involve the asymptotic fraction of time spent on particular edges. Basic ingredients are known FKG-type inequalities and known negative associations for determinantal processes.

Original language	English
Pages (from-to)	753-763
Number of pages	11
Journal	Electronic Communications in Probability
Volume	16
DOIs	https://doi.org/10.1214/ECP.v16-1683
State	Published - 1 Jan 2011

Keywords

FKG inequalities
Reinforced random walk
Spanning trees

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10.1214/ECP.v16-1683

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title = "Correlation inequalities for edge-reinforced random walk",

abstract = "We prove correlation inequalities for linearly edge-reinforced random walk. These correlation inequalities concern the first entry tree, i.e. the tree of edges used to enter any vertex for the first time. They also involve the asymptotic fraction of time spent on particular edges. Basic ingredients are known FKG-type inequalities and known negative associations for determinantal processes.",

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AB - We prove correlation inequalities for linearly edge-reinforced random walk. These correlation inequalities concern the first entry tree, i.e. the tree of edges used to enter any vertex for the first time. They also involve the asymptotic fraction of time spent on particular edges. Basic ingredients are known FKG-type inequalities and known negative associations for determinantal processes.

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DO - 10.1214/ECP.v16-1683

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VL - 16

SP - 753

EP - 763

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

ER -

Correlation inequalities for edge-reinforced random walk

Abstract

Keywords

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