Two-sided heat kernel bounds for 8/3-Liouville Brownian motion
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 γ=8/3 in terms of the 8/3-LQG metric which are sharp up to a polylogarithmic factor in the exponential.
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