Random Conformal Welding for Finitely Connected Regions

Shi-Yi Lan () and Wang Zhou ()
Additional contact information
Shi-Yi Lan: Guangxi University for Nationalities
Wang Zhou: National University of Singapore

Journal of Theoretical Probability, 2019, vol. 32, issue 2, 659-683

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

Keywords: Random welding; Quasiconformal mapping; Gaussian free field; SLE; 30C62; 60D05 (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-018-0874-5 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:32:y:2019:i:2:d:10.1007_s10959-018-0874-5

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-018-0874-5

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().