I study hyperbolic dynamical systems, probability theory and mathematical statistial physics.
In particular, I am interested in statistical properties of singular hyperbolic systems, such as Sinai billiards,
and in mathematical models of heat transport, both in large deterministic systems and in stochastic interacting particle systems.

Together with Dmitry Dolgopyat, we proved
that the asymptotic density of non-interacting particles in a long Lorentz tube (including the non-equilibrium case),
is governed by the heat equation. Next, one would like to consider the
case of small, rarely interacting Lorentz particles.
We have studied the first time of interaction of two such particles.

Also with Dmitry Dolgopyat, we proved
a local central limit theorem and mixing for certain hyperbolic flows preserving a
finite measure
and Krickeberg mixing in case of infinite measure.

Together with Domokos Szász and Tamás Varjú, we computed
the tail distribution of the free path lengths in high dimensional Loretnz gases with infinite horizon.
In particular, we proved the corresponding geometric conjectures of Carl Dettmann.

I studied some asymptotic properties of various random walks. For instance, I
computed the asymptotic
number of visited points of a random walk with internal states.