Random conformal welding for finitely connected regions

2014/10/23 by Shiyi Lan, Shi-Yi Lan, Zhou Wang +3
Mathematics · #30C62 #60D05 #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities #Probability (math.PR) #math.CV #math.PR #msc:30C62 #msc:60D05

paper · pdf · doi:10.48550/arxiv.1410.6417

25 pages

arxiv created 2014/10/23 · openalex publication_date 2014/10/23 · arxiv updated 2014/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a finitely connected region Ω of the Riemann sphere whose complement consists of m mutually disjoint closed disks U_j, the random homeomorphism h_j on the boundary component ∂ U_j is constructed using the exponential Gaussian free field. The existence and uniqueness of random conformal welding of Ω with h_j is established by investigating a non-uniformly elliptic Betrami equation with a random complex dilatation. This generalizes the result of Astala, Jones, Kupiainen and Saksman to multiply connected domains.

Citations

• Factorisation of conformal maps on finitely connected domains
• The boundary correspondence under quasiconformal mappings

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