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Conformally invariant loop measures

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We will discuss several aspects of a conjecture by Kontsevich and Suhov regarding existence and uniqueness of a one parameter family of conformally invariant measures on simple loops (conjecturally related to the SLE family). The most natural case (zero central charge i.e. SLE parameter kappa=8/3) was understood in a beautiful paper of Werner predating the conjecture. Dubédat and myself constructed an example of such a loop measure in non-zero central charge (kappa=2 i.e. c=-2).

This talk is part of the Probability series.

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