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research article
Extremal Distance And Conformal Radius Of A Cle4 Loop
March 1, 2022
Consider CLE4 in the unit disk, and let l be the loop of the CLE4 surrounding the origin. Schramm, Sheffield and Wilson determined the law of the conformal radius seen from the origin of the domain surrounded by l. We complement their result by determining the law of the extremal distance between and the boundary of the unit disk. More surprisingly, we also compute the joint law of these conformal radius and extremal distance. This law involves first and last hitting times of a one-dimensional Brownian motion. Similar techniques also allow us to determine joint laws of some extremal distances in a critical Brownian loop-soup cluster.
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Type
research article
Web of Science ID
WOS:000773518500003
Authors
Publication date
2022-03-01
Publisher
Published in
Volume
50
Issue
2
Start page
509
End page
558
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
April 11, 2022