Liouville heat kernel upper bounds at large distances

2022/10/11 by Yu, Yang
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2210.05255

Abstract

We show that the Liouville heat kernel decays fast at large distances. In particular, the Liouville semigroup T_t is C₀-Feller, where C₀ is the space of real-valued continuous functions on \mathbb C vanishing at infinity.

Related

• Two-sided heat kernel bounds for √(8/3)-Liouville Brownian motion
• Continuity and estimates of the Liouville heat kernel with applications to spectral dimensions
• Sharp gradient estimate and Yau's Liouville theorem for the heat equation on noncompact manifolds
• Heat Kernel Estimates for Schrödinger Operators in the Domain Above a Bounded Lipschitz Function
• Note on basic features of large time behaviour of heat kernels