Ilya Gekhtman

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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…