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.

I co-organize the UVa Probability seminar.

I am founder of and coordinate activities for Women in Probability.

I am faculty coordinator for the UVa Math Ambassadors.

All course materials for classes I am teaching may be found on the UVa Canvas course page.

Charlottesville, VA 22903 USA

Tel: (434) 982-2782

Fax: (434) 982-3084

Office: 205 Kerchof

E-mail: melcher "at" virginia.edu