Defining SLE in multiply connected domains with the Brownian loop\n measure

2011/08/22 by Gregory F. Lawler, Lawler, Gregory F. · 2 citations
Mathematics · Medicine · #60J67 #Algebraic structures and combinatorial models #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR) #Rings, Modules, and Algebras #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1108.4364

openalex publication_date 2011/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define the Schramm-Loewner evolution (SLE) in multiply connected domains\nfor kappa \≤ 4 using the Brownian loop measure. We show that in the case of\nthe annulus, this is the same measure obtained recently by Dapeng Zhan. We use\nthe loop formulation to give a different derivation of the partial differential\nequation for the partition function for the annulus.\n

Citations

• Contour lines of the two-dimensional discrete Gaussian free field

Cited by

• Arm events in critical planar loop soups
• Disconnection probability of Brownian motion on an annulus

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