Uniqueness of Malliavin—Kontsevich—Suhov measures

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• Antoine Jego (EPFL - Ecole Polytechnique Fédérale de Lausanne)
• Monday 28 October 2024, 15:30-16:30
• Seminar Room 1, Newton Institute.

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SSDW03 - Geometry, occupation fields, and scaling limits

About 20 years ago, Kontsevich & Suhov conjectured the existence and uniqueness of a family of measures on the set of Jordan curves, characterised by conformal invariance and a restriction-type property. This conjecture was motivated by (seemingly unrelated) works of Schramm, Lawler & Werner on Schramm—Loewner evolutions (SLE), and Malliavin, Airault & Thalmaier on “unitarising measures”. The existence of this family was settled by works of Werner—Kemppainen and Zhan, using a loop version of SLE . The uniqueness was recently obtained in a joint work with Baverez. I will start by reviewing the different notions involved before giving some ideas of our proof of uniqueness: in a nutshell, we construct a family of “orthogonal polynomials” which completely characterises the measure. I will discuss the broader context in which our construction fits, namely the conformal field theory associated with SLE .

This talk is part of the Isaac Newton Institute Seminar Series series.

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