Random conformal welding for finitely connected regions

Abstract

Given a finitely connected region $\Omega$ of the Riemann sphere whose complement consists of $m$ mutually disjoint closed disks ${\bar{U}}_j$, the random homeomorphism $h_j$ on the boundary component $\partial U_j$ is constructed using the exponential Gaussian free field. The existence and uniqueness of random conformal welding of $\Omega$ 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.

25 pages

References in corpus (3)

• Critical percolation in the plane
• Factorisation of conformal maps on finitely connected domains
• Random Conformal Weldings at criticality