Abstract Continuing from Choi (2022), we study random walks on metric spaces with
contracting elements. We prove that random subgroups of the isometry group of a metric …

We study random walks on the lampshuffler group FSym (H)⋊ H, where H is a finitely
generated group and FSym (H) is the group of finitary permutations of H. We show that for …

We provide a simple criterion for an element of the mapping class group of a closed surface
to be a normal generator for the mapping class group. We apply this to show that every …

Let M be a hyperbolic fibered 3–manifold. We study properties of sequences (S α n, ψ α n) of
fibers and monodromies for primitive integral classes in the fibered cone of M. The main …

We study properties of generic elements of groups of isometries of hyperbolic spaces. Under
general combinatorial conditions, we prove that loxodromic elements are generic (ie, they …

For any countable group with infinite conjugacy classes we construct a family of forests on
the group. For each of them there is a random walk on the group with the property that its …

For any countable group with infinite conjugacy classes we construct a family of forests on
the group. For each of them there is a random walk on the group with the property that its …

In this paper, we study the normal generation of the mapping class group. We first show that
a mapping class is a normal generator if its restriction on the invariant subsurface normally …

Asymptotic properties and Poisson boundaries of wreath products Page 1 Préparée à l’École
Normale Supérieure de Paris Asymptotic properties and Poisson boundaries of wreath …

Reid asked whether all convex‐cocompact subgroups of mapping class groups are
separable. Using a construction of Manning–Mj–Sageev, we give examples of separable …