Two-sided heat kernel bounds for $\sqrt{8/3}$-Liouville Brownian motion

Published 17 Jul 2025 in math.PR, math-ph, math.CV, and math.MP | (2507.13269v1)

Abstract: Liouville Brownian motion (LBM) is the canonical diffusion process on a Liouville quantum gravity (LQG) surface. In this work, we establish upper and lower bounds for the heat kernel for LBM when $\gamma=\sqrt{8/3}$ in terms of the $\sqrt{8/3}$-LQG metric which are sharp up to a polylogarithmic factor in the exponential.

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