Two-sided heat kernel bounds for $\sqrt{8/3}$-Liouville Brownian motion
Probability
2026-04-16 v2 Mathematical Physics
Complex Variables
math.MP
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 in terms of the -LQG metric which are sharp up to a polylogarithmic factor in the exponential.
Cite
@article{arxiv.2507.13269,
title = {Two-sided heat kernel bounds for $\sqrt{8/3}$-Liouville Brownian motion},
author = {Sebastian Andres and Naotaka Kajino and Konstantinos Kavvadias and Jason Miller},
journal= {arXiv preprint arXiv:2507.13269},
year = {2026}
}
Comments
134 pages, 8 figures; some typos have been fixed, the list of references has been updated, and a paragraph describing special features of $\sqrt{8/3}$-LQG has been added in the introduction