On conformally invariant CLE explorations

Abstract

We study some conformally invariant dynamic ways to construct the Conformal Loop Ensembles with simple loops introduced in earlier papers by Sheffield, and by Sheffield and Werner. One outcome is a conformally invariant way to measure a distance of a CLE(4) loop to the boundary "within" the CLE(4), when one identifies all points of each loop.

to appear in Comm. Math. Phys

References in corpus (1)

• Reversibility of chordal SLE

Cited by in corpus (10)

• Quantum Loewner Evolution
• CLE percolations
• On bounded-type thin local sets of the two-dimensional Gaussian free field
• The Hausdorff dimension of the CLE gasket
• Connection probabilities for conformal loop ensembles
• The random pseudo-metric on a graph defined via the zero-set of the Gaussian free field on its metric graph
• Coupling the Gaussian free fields with free and with zero boundary conditions via common level lines
• The trunks of CLE(4) explorations
• Liouville quantum gravity weighted by conformal loop ensemble nesting statistics
• Distances on the ${\mathrm{CLE}}_4$, critical Liouville quantum gravity and $3/2$-stable maps