We study random walks on the isometry group of a Gromov hyperbolic space or Teichmüller
space. We prove that the translation lengths of random isometries satisfy a central limit …

We establish central limit theorems for an action of a group. Our techniques allow us to
remove the usual assumptions of properness and smoothness of the space, or …

Using techniques from ergodic theory and symbolic dynamics, we derive statistical limit laws
for real valued functions on hyperbolic groups. In particular, our results apply to convex …

We consider the geodesic flow for a rank one non-positive curvature closed manifold. We
prove an asymptotic version of the Central Limit Theorem for families of measures …

In this note, we present new asymptotic estimates comparing the word length and geodesic
length of closed geodesics on surfaces with (variable) negative sectional curvatures. In …

Let A, B be matrices in ${\mathrm {S}\mathrm {L}} _ {2}\mathbb {R} $ having trace greater
than or equal to 2. Assume the pair A, B is coherently oriented, that is, can be conjugated to …

Abstract Athreya, Bufetov, Eskin and Mirzakhani have shown the number of mapping class
group lattice points intersecting a closed ball of radius $ R $ in Teichm\"{u} ller space is …

The work presented in this thesis is concerned with quantifying, in various different senses,
how natural quantities associated to hyperbolic groups grow and distribute. Hyperbolic …