46 citations · 89 across the 17 of their papers we have counts for
21 papers
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…
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…
Localized bounds on log-derivatives of the heat kernel on incomplete Riemannian manifolds
Robert W. Neel, Ludovic Sacchelli
Bounds on the logarithmic derivatives of the heat kernel on a compact Riemannian manifolds have been long known, and were recently extended, for the log-gradient and log-Hessian, t…
Variations of the sub-Riemannian distance on Sasakian manifolds with applications to coupling
Fabrice Baudoin, Erlend Grong, Robert Neel +1
On Sasakian manifolds with their naturally occurring sub-Riemannian structure, we consider parallel and mirror maps along geodesics of a taming Riemannian metric. We show that thes…
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…
Radial processes for sub-Riemannian Brownian motions and applications
Fabrice Baudoin, Erlend Grong, Kazumasa Kuwada +2
We study the radial part of sub-Riemannian Brownian motion in the context of totally geodesic foliations. Itô's formula is proved for the radial processes associated to Riemannian…