Uniqueness of generalized conformal restriction measures and Malliavin-Kontsevich-Suhov measures for $c \in (0,1]$

Gefei Cai; Yifan Gao

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arXiv · 2502.05890

Uniqueness of generalized conformal restriction measures and Malliavin-Kontsevich-Suhov measures for $c \in (0,1]$

Gefei Cai·Yifan Gao

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Abstract

In this paper, we present a unified approach to establish the uniqueness of generalized conformal restriction measures with central charge $c \in (0, 1]$ 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 $c \in (0,1]$, which was recently obtained in [Baverez-Jego, arXiv:2407.09080] for all $c \leq 1$ from a CFT framework of SLE loop measures. In contrast, though only valid for $c \in (0,1]$, our approach provides additional probabilistic insights, as it directly links natural quantities of MKS measures to loop-soup observables.

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Gefei Cai, Yifan Gao. 2025-02-09. Uniqueness of generalized conformal restriction measures and Malliavin-Kontsevich-Suhov measures for $c \in (0,1]$. https://arxiv.org/abs/2502.05890

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