Uniqueness of Malliavin-Kontsevich-Suhov measures
Date(s) : 03/12/2024 iCal
14h30 - 15h30
Abstract: 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 another property called « conformal restriction ». This conjecture was motivated by (seemingly unrelated) works of Schramm, Lawler & Werner on stochastic 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 Jego.
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 characterise the measure. In the remaining time, I will discuss the broader context in which our construction fits, namely the conformal field theory associated with SLE.
Emplacement
I2M Saint-Charles - Salle de séminaire
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