Existence and Uniqueness of Nonsimple Multiple SLE

We prove the existence and uniqueness of multiple SLE κ associated with any given link pattern for κ ∈ ( 4 , 6 ] . We also have the uniqueness for κ ∈ ( 6 , 8 ) . The multiple SLE κ law is constructed by first inductively constructing a σ -finite multiple SLE κ measure and then normalizing the measu...

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Bibliographic Details
Published inJournal of statistical physics Vol. 191; no. 8
Main Author Zhan, Dapeng
Format Journal Article
LanguageEnglish
Published New York Springer US 11.08.2024
Springer
Springer Nature B.V
Subjects
Mathematical and Computational Physics
Partitions (mathematics)
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Uniqueness
Irreducible Markov chain
Multiple SLE
Partition function
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Summary:We prove the existence and uniqueness of multiple SLE κ associated with any given link pattern for κ ∈ ( 4 , 6 ] . We also have the uniqueness for κ ∈ ( 6 , 8 ) . The multiple SLE κ law is constructed by first inductively constructing a σ -finite multiple SLE κ measure and then normalizing the measure whenever it is finite. The total mass of the measure satisfies the conformal covariance, asymptotics and PDE for multiple SLE κ partition functions in the literature subject to the assumption that it is smooth.
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ISSN:1572-9613
0022-4715
1572-9613
DOI:10.1007/s10955-024-03306-8