Random conformal welding for finitely connected regions. (English) Zbl 1417.30013
Summary: 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 K. Astala et al. [Acta Math. 207, No. 2, 203–254 (2011; Zbl 1253.30032)] to multiply connected domains.
MSC:
| 30C62 | Quasiconformal mappings in the complex plane |
| 60D05 | Geometric probability and stochastic geometry |
Citations:
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