4 papers · 1 filter
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…
Spectral gap for products and a strong normal subgroup theorem
Uri Bader, Tsachik Gelander, Arie Levit
We establish a general spectral gap theorem for actions of products of groups which may replace Kazhdan's property (T) in various situations. As a main application, we prove that a…
Surface groups are flexibly stable
Nir Lazarovich, Arie Levit, Yair Minsky
We show that surface groups are flexibly stable in permutations. This is the first non-trivial example of a non-amenable flexibly stable group. Our method is purely geometric and r…
Spectral gap and character limits in arithmetic groups
Arie Levit, Raz Slutsky, Itamar Vigdorovich
We establish vanishing results for limits of characters in various discrete groups, most notably irreducible lattices in higher rank semisimple Lie groups. As an application, we sh…