My research interests intersect probability, geometry, and analysis. More particularly, they include infinite-dimensional analysis, Gaussian measures and processes, stochastic differential equations on Lie groups (and sometimes more general manifolds), Markov processes and semigroups, differential operators and hypoellipticity theory. My articles on arXiv.
Functional inequalities for a family of infinite-dimensional diffusions with degenerate noise with F. Baudoin, M. Gordina, D. Herzog, and J. Kim
arXiv: 2311.01440, 2023.
Large deviations principle for sub-Riemannian random walks with M. Gordina and J. Wang
arXiv: 2210.05817, 2022.
Quasi-invariance for infinite-dimensional Kolmogorov diffusions with F. Baudoin and M. Gordina
Potential Analysis, 2023.
Stochastic integrals and Brownian motion on abstract nilpotent Lie groups
Journal of the Mathematical Society of Japan, 73, 1159-1185, 2021.
Small-time asymptotics for subelliptic Hermite functions on SU(2) and the CR sphere with J. Campbell
Potential Analysis, 53, 1063–1095, 2020.
Convergence rates of the empirical spectral measure of unitary Brownian motion with E. Meckes
Annales Henri Lebesgue, 1, 247-265, 2018.
Hypoelliptic heat kernels on infinite-dimensional Heisenberg groups with B. Driver and N. Eldredge
Transactions of the AMS, 368, 989-1022, 2016.
Small deviations for time-changed Brownian motions and applications to second-order chaos with D. Dobbs
Electronic Journal of Probability, 19, 1-23, 2014.
Smoothness of heat kernel measures on infinite-dimensional Heisenberg-like groups with D. Dobbs
Journal of Functional Analysis, 264, 2206-2223, 2013.
Quasi-invariance for heat kernel measures on sub-Riemannian infinite-dimensional Heisenberg groups with F. Baudoin and M. Gordina
Transactions of the AMS, 365, 4313-4350, 2013.
A subelliptic Taylor isomorphism on infinite-dimensional Heisenberg groups with M. Gordina
Probability Theory and Related Fields, 155, 379-426, 2013.
Heat kernel analysis on semi-infinite Lie groups
Journal of Functional Analysis, 257, 3552-3592, 2009.
Malliavin calculus for Lie group-valued Wiener functions with note
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 12, 67-89, 2009.
Hypoelliptic heat kernel inequalities on Lie groups
Stochastic Processes and their Applications, 118, 368-388, 2008.
Hypoelliptic heat kernel inequalities on the Heisenberg group with B. Driver
Journal of Functional Analysis, 221, 340-365, 2005.