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

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 $\gamma =\sqrt{8\mathrm{/}3}$ in terms of the $\sqrt{8\mathrm{/}3}$-LQG metric which are sharp up to a polylogarithmic factor in the exponential.