Probability and Mathematical Physics Seminar

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Short time asymptotics for Liouviille heat kernel and graph distances

Speaker: Ofer Zeitouni, Courant Institute/Weizmann Institute

Location: Warren Weaver Hall 512

Date: Friday, October 5, 2018, 11 a.m.

Synopsis:

The Liouville Brownian motion is Brownian motion in 2D, time changed by the exponential of the Gaussian free field along its trajectory. In recent work with Jian Ding and Fuxi Zhang, we established the existence of scaling exponent for the (logarithmic) short time asymptotics of the heat kernel, and linked the exponent to the scaling exponent of the graph distance for Liouville quantum gravity., which we also proved exists. I will describe this and some related developments.