Integrability of the Schramm-Loewner evolution via conformal welding of random surfaces

Abstract: The Schramm-Loewner evolution is a one-parameter family of random fractal curves which describe the scaling limit of statistical physics models. We derive an explicit formula for the moments of the derivative of a particular uniformizing conformal map associated with an SLE. The problems is hard to approach via classical Ito calculus methods, and our proof relies instead on conformal welding of Liouville quantum gravity surfaces along with integrability results from Liouville conformal field theory. Joint work with Morris Ang and Xin Sun.

analysis of PDEsprobability

Audience: researchers in the discipline

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Stochastic PDEs and their friends

Series comments: We are organizing a three day online workshop devoted to recent developments in SPDEs and related topics. Please complete the registration form at forms.gle/G9Xw942iVNNgB4SLA if you would like to take part in the conference.

Confirmed speakers:

Yuri BAKHTIN (NYU)

Ajay CHANDRA (Imperial)

Dan CRISAN (Imperial)

Nina HOLDEN (ETH Zurich)

Kostantin KHANIN (U Toronto)

Davar KHOSHNEVISAN (University of Utah)

Nicolai KRYLOV (University of Minnesota)

Jonathan MATTINGLY (Duke)

Leonid MYTNIK (Technion)

Nicolas PERKOWSKI (Free U Berlin)

Ellen POWELL (Durham University)

Jeremy QUASTEL (U Toronto)

Daniel REMENIK (Universidad de Chile)

Armen SHIRIKYAN (University of Cergy-Pontoise)

Gigliola STAFFILANI (MIT)

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