5 citations · 12 across the 10 of their papers we have counts for
12 papers
Convex geometries representable by at most 5 circles on the plane
PolyMath REU Convex Geometries Collaboration, Kira Adaricheva, Madina Bolat +18
A convex geometry is a closure system satisfying the anti-exchange property. In this work we document all convex geometries on 4- and 5-element base sets with respect to their repr…
Approximation of Riemannian measures by Stein's method
James Thompson
In this article, we present the theoretical basis for an approach to Stein's method for probability distributions on Riemannian manifolds. Using a semigroup representation for the…
Exponential integrability and exit times of diffusions on sub-Riemannian and metric measure spaces
Anton Thalmaier, James Thompson
In this article we derive moment estimates, exponential integrability, concentration inequalities and exit times estimates for canonical diffusions in two settings each beyond the…
Functional inequalities for Feynman-Kac semigroups
James Thompson
Using the tools of stochastic analysis, we prove various gradient estimates and Harnack inequalities for Feynman-Kac semigroups with possibly unbounded potentials. One of the main…
Uniform gradient estimates on manifolds with a boundary and applications
Li-Juan Cheng, Anton Thalmaier, James Thompson
We revisit the problem of obtaining uniform gradient estimates for Dirichlet and Neumann heat semigroups on Riemannian manifolds with boundary. As applications, we obtain isoperime…
Functional inequalities on manifolds with non-convex boundary
Li-Juan Cheng, Anton Thalmaier, James Thompson
In this article, new curvature conditions are introduced to establish functional inequalities including gradient estimates, Harnack inequalities and transportation-cost inequalitie…
Quantitative -estimates by Bismut formulae
Li-Juan Cheng, Anton Thalmaier, James Thompson
For a function and an elliptic operator , we prove a quantitative estimate for the derivative in terms of local bounds on and . An integral version of thi…
Derivative and divergence formulae for diffusion semigroups
Anton Thalmaier, James Thompson
For a semigroup generated by an elliptic operator on a smooth manifold , we use straightforward martingale arguments to derive probabilistic formulae for , not…
Derivatives of Feynman-Kac Semigroups
James Thompson
We prove Bismut-type formulae for the first and second derivatives of a Feynman-Kac semigroup on a complete Riemannian manifold. We derive local estimates and give bounds on the lo…
First Order Feynman-Kac Formula
Xue-Mei Li, James Thompson
We study the parabolic integral kernel associated with the weighted Laplacian and the Feynman-Kac kernels. For manifold with a pole we deduce formulas and estimates for them and fo…
Brownian bridges to submanifolds
James Thompson
We introduce and study Brownian bridges to submanifolds. Our method involves proving a general formula for the integral over a submanifold of the minimal heat kernel on a complete…
Brownian motion and the distance to a submanifold
James Thompson
We present a study of the distance between a Brownian motion and a submanifold of a complete Riemannian manifold. We include a variety of results, including an inequality for the L…