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-Jego, arXiv:2407.09080] 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.
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