Two-Sided Heat Kernel Bounds for $\Sqrt {8/3} $-Liouville Brownian Motion
Time: 2026-01-15
Published By: Xiaoni Tan
Speaker(s): Naotaka Kajino (Kyoto University)
Time: 09:00-10:00 January 20, 2026
Venue: Online
Abstract:
The $\gamma$-Liouville Brownian motion ($\gamma$-LBM) is the canonical diffusion process on a $\gamma$-Liouville quantum gravity ($\gamma$-LQG) surface, where $\gamma \in (0,2)$ is a parameter. The $\sqrt{8/3}$-LQG sphere, considered as (the isomorphism class of) a random compact metric measure space, has been proved by Miller and Sheffield (2021) to have the same law as the Brownian sphere, which in turn was proved by Le Gall (2013) and Miermont (2013) to appear as the scaling limit of a uniform random $n$-face quadangulation of the sphere as $n$ tends to infinity.
This talk will present the main result of arXiv:2507.13269 establishing, for the heat kernel of the $\sqrt{8/3}$-LBM on the $\sqrt{8/3}$-LQG sphere, two-sided off-diagonal sub-Gaussian bounds which are sharp up to polylogarithmic factors in the exponential. This is joint work with Sebastian Andres (Technische Universit\"{a}t Braunschweig), Konstantinos Kavvadias (Massachusetts Institute of Technology) and Jason Miller (University of Cambridge).
Zoom Meeting ID: 181 155 584
