My research lies in the field of probability theory, with an emphasis on interacting particle systems and stochastic analysis. Stochastic billiards is another major focus of my work. A more recent research direction has been the application of methods from interacting particle systems to problems in optimization and Gibbs sampling.
A few guiding themes unite my work. One is to understand the emergence of universality phenomena at large space- and time-scales in random dynamical systems. A second theme is to describe the ergodic structures of random dynamical systems, characterizing their equilibrium and mixing behavior. In developing these themes, I am especially interested in systems of interacting particles and related models which are high-dimensional or which exhibit a substantial amount of determinism, as these systems push our current theoretical understanding to the limit, requiring new techniques to be approached effectively. A further motivation for studying these systems is that high-dimensional and `semi-deterministic' phenomena are closer to the areas of application which we encounter in the real world.
"Archimedes' principle for a gas of non-spherical particles." With Krzysztof Burdzy and Jacek Małecki. In preparation.
"Strong existence, pathwise uniqueness and chains of collisions in infinite Brownian particle systems." With Sayan Banerjee and Amarjit Budhiraja. Submitted. [arXiv]
"Fluctuations of the Atlas model from inhomogeneous stationary profiles." With Sayan Banerjee and Amarjit Budhiraja. To appear in Annals of Probability. [arXiv]
"Semi-deterministic processes with applications in random billiards." Transactions of the AMS, 387 (2025) 5927-5980. [journal] [arXiv]
"Rough Collisions." Memoirs of the AMS, 304 (2024), no. 1533. [journal] [arXiv]