Uniqueness of generalized conformal restriction measures and Malliavin–Kontsevich–Suhov measures for c∈(0,1]
Abstract
In this paper, we present a unified approach to establish the uniqueness of generalized conformal restriction measures with central charge c∈(0,1] in both chordal and radial cases, by relating these measures to the Brownian loop soup. Our method also applies to the uniqueness of the Malliavin–Kontsevich–Suhov loop measures for c∈(0,1], which was recently obtained in (Baverez and Jego (2024)) for all c≤1 from a CFT framework of SLE loop measures. In contrast, though only valid for c∈(0,1], our approach provides additional probabilistic insights, as it directly links natural quantities of MKS measures to loop-soup observables.
Fields of Study & Subjects
Advanced Algebra and Geometry
Analytic and geometric function theory
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- The Annals of Probability
- Volume
- 54
- Issue
- 4
- Publication date
- 30 June 2026
- Language
- EN