Conformal restriction: the radial case

TL;DR

This paper characterizes all random sets satisfying radial conformal restriction, extending the chordal case results of Lawler, Schramm, and Werner to the radial setting.

Contribution

It provides a complete description of radial conformal restriction sets, filling a gap in the understanding of conformal invariance in different geometric configurations.

Findings

All radial conformal restriction sets are characterized.

The radial case parallels the chordal case results.

Provides a foundation for further studies in radial conformal invariance.

Abstract

We describe all random sets that satisfy the radial conformal restriction property, therefore providing the analogue in the radial case of results of Lawler, Schramm and Werner in the chordal case.