2010/12/23 by Dmitry Beliaev, Beliaev, Dmitry, Fredrik Viklund +2
Mathematics · Physics and Astronomy · #Complex Variables (math.CV) #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.CV #math.PR
paper · pdf · doi:10.48550/arxiv.1012.5206
Rewritten and expanded with several new results; 15 pages
openalex publication_date 2010/12/23 · arxiv created 2011/09/18 · arxiv updated 2011/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Simmons and Cardy recently predicted a formula for the probability that the chordal SLE(8/3) path passes to the left of two points in the upper half-plane. In this paper we give a rigorous proof of their formula. Starting from this result, we derive explicit expressions for several natural connectivity functions for SLE(8/3) bubbles conditioned to be of macroscopic size. By passing to a limit with such a bubble we construct a certain chordal restriction measure and in this way obtain a proof of a formula for the probability that two given points are between two commuting SLE(8/3) paths. The one-point version of this result has been predicted by Gamsa and Cardy. Finally, we derive an integral formula for the second moment of the area of an SLE(8/3) bubble conditioned to have radius 1. We evaluate the area integral numerically and relate its value to a hypothesis that the area follows the Airy distribution.