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Transition probabilities for infinite two-sided loop-erased random walks
Brooklyn College, City University of New York, United States of America..
University of Chicago, United States of America..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2019 (English)In: Electronic Journal of Probability, Vol. 24, article id 139Article in journal (Refereed) Published
Abstract [en]

The infinite two-sided loop-erased random walk (LERW) is a measure on infinite self-avoiding walks that can be viewed as giving the law of the “middle part” of an infinite LERW loop going through 0" role="presentation">0 and ∞" role="presentation">∞. In this note we derive expressions for transition probabilities for this model in dimensions d≥2" role="presentation">d≥2. For d=2" role="presentation">d=2 the formula can be further expressed in terms of a Laplacian with signed weights acting on certain discrete harmonic functions at the tips of the walk, and taking a determinant. The discrete harmonic functions are closely related to a discrete version of z↦z" role="presentation">z↦z√.

Place, publisher, year, edition, pages
2019. Vol. 24, article id 139
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-268285DOI: 10.1214/19-EJP376Scopus ID: 2-s2.0-85076316530OAI: oai:DiVA.org:kth-268285DiVA, id: diva2:1415296
Note

QC 20200318

Available from: 2020-03-18 Created: 2020-03-18 Last updated: 2020-03-18Bibliographically approved

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Viklund, Fredrik

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