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Hypergeometric SLE with κ = 8: Convergence of UST and LERW in topological rectangles
School of Mathematical Sciences, Shenzhen University, Shenzhen, China.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Probability, Mathematical Physics and Statistics.
Yau Mathematical Sciences Center and Department of Mathematics, Tsinghua University, Beijing, China.
2025 (English)In: Annales de l'I.H.P. Probabilites et statistiques, ISSN 0246-0203, E-ISSN 1778-7017, Vol. 61, no 2, p. 1163-1211Article in journal (Refereed) Published
Abstract [en]

We consider uniform spanning tree (UST) in topological rectangles with alternating boundary conditions. The Peano curves associated to the UST converge weakly to hypergeometric SLE8, denoted by hSLE8. From the convergence result, we obtain the continuity and reversibility of hSLE8 as well as an interesting connection between SLE8 and hSLE8. The loop-erased random walk (LERW) branch in the UST converges weakly to SLE2(−1,−1;−1,−1). We also obtain the limiting joint distribution of the two end points of the LERW branch.

Place, publisher, year, edition, pages
Institute of Mathematical Statistics , 2025. Vol. 61, no 2, p. 1163-1211
Keywords [en]
Loop-erased random walk, Schramm Loewner evolution, Uniform spanning tree
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-364142DOI: 10.1214/23-AIHP1446ISI: 001523086100013Scopus ID: 2-s2.0-105005968791OAI: oai:DiVA.org:kth-364142DiVA, id: diva2:1964098
Note

QC 20250604

Available from: 2025-06-04 Created: 2025-06-04 Last updated: 2025-10-10Bibliographically approved

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Liu, Mingchang

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