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 Beltrami equation with a random complex dilatation. This generalizes the result of Astala, Jones, Kupiainen and Saksman to multiply connected domains.
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