Ilya Gekhtman

collaborators

5 papers

math.DS2026

The Structure of Almost Stationary Measures

Ilya Gekhtman, Simon Machado, Omri Solan +1

Let $G$ be a higher-rank simple Lie group acting on a space $X$ . A theorem of Nevo and Zimmer asserts that every ergodic stationary probability measure on $X$ is either $G$ -invaria…

math.DS2026

Applications of Almost Stationarity I: Quantitative Growth of Injectivity Radius and StÃ¼ck-Zimmer Theorem

Ilya Gekhtman, Simon Machado, Omri Solan +1

Fraczyk and Gelander proved in \cite{FG} that for any simple Lie group $G$ of high rank and for every non-lattice discrete subgroup $I^ \leq G$ , the injectivity radius of points in…

math.DS2026

Topology and dynamics of unimodular random hyperbolic manifolds

Ilya Gekhtman, Nir Lazarovich, Arie Levit +1

We investigate the relationship between the space of ends of a unimodular random hyperbolic manifold and the dynamics of its geodesic flow. We show that having two ends of infinite…

math.PR2026

Space-time boundaries for random walks and their application to operator algebras

Adam Dor-On, Ilya Gekhtman, Pavel Prudnikov

We investigate the Martin boundary of the space-time Markov chain associated to a finitely supported random walk $(I^, I^¼)$ with spectral radius $I ¨ $ and relate it to several class…

math.GR2025

Stationary random subgroups in negative curvature

Ilya Gekhtman, Arie Levit

We show that discrete stationary random subgroups of isometry groups of Gromov hyperbolic spaces have full limit sets as well as critical exponents bounded from below. This informa…