The nested simple conformal loop ensembles in the Riemann sphere

Abstract

Simple conformal loop ensembles (CLE) are a class of random collection of simple non-intersecting loops that are of particular interest in the study of conformally invariant systems. Among other things related to these CLEs, we prove the invariance in distribution of their nested "full-plane" versions under the inversion $z\mapsto 1/z$.

V2: minor edits

References in corpus (2)

• Conformal radii for conformal loop ensembles
• Random soups, carpets and fractal dimensions

Cited by in corpus (3)

• Level Lines of Gaussian Free Field II: Whole-Plane GFF
• Simple CLE in Doubly Connected Domains
• Multi-arm incipient infinite clusters in 2D: scaling limits and winding numbers