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.  Most of my articles are on arXiv.

• Functional inequalities for a family of infinite-dimensional diffusions with degenerate noise with F. Baudoin, M. Gordina, D. Herzog, and J. Kim
  accepted to Journal of Functional Analysis, 2024.

• Large deviations principle for sub-Riemannian random walks with M. Gordina, D. Mikulincer, and J. Wang
  arXiv: 2210.05817, 2022.

• Quasi-invariance for infinite-dimensional Kolmogorov diffusions with F. Baudoin and M. Gordina
  Potential Analysis, 60, 807-831, 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.