3 papers
math.PR2026
Sharp Riemannian heat kernel estimates on the cut locus and the Parabolic Anderson model
Hongyi Chen, Robert Neel, Cheng Ouyang
Using sharp global heat kernel bounds and geodesic comparison geometry, we show that the Dalang condition for well-posedness of the parabolic Anderson model with measure-valued ini…
math.PR2025
Uniform, localized asymptotics for sub-Riemannian heat kernels, their logarithmic derivatives, and associated diffusion bridges
Robert W. Neel, Ludovic Sacchelli
We show that the small-time asymptotics of the sub-Riemannian heat kernel, its derivatives, and its logarithmic derivatives can be localized, allowing them to be studied even on in…
math.PR2025
Non-Markovian maximal couplings and a vertical reflection principle on a class of sub-Riemannian manifolds
Liangbing Luo, Robert W. Neel
We develop an approach to constructing non-Markovian, non-co-adapted couplings for sub-Riemannian Brownian motions in sub-Riemannian manifolds with large symmetry groups by treatin…