5 papers
Random walks on cocompact Fuchsian and Kleinian groups
Nikolay Bogachev, Peter Kosenko, Giulio Tiozzo
The question of the singularity at infinity of the hitting measure of random walks has a long history, originating from the work of Furstenberg in the 1960s. In 2011, Kaimanovich a…
The Poisson boundary of discrete subgroups of semisimple Lie groups without moment conditions
Kunal Chawla, Behrang Forghani, Joshua Frisch +1
We show that the Poisson boundary of random walks of finite entropy on Zariski-dense discrete subgroups of semisimple Lie groups equals the Furstenberg boundary of the correspondin…
Singularity of Furstenberg measure for infinite covolume discrete subroups in higher rank
Homin Lee, Wouter Van LimBeek, Giulio Tiozzo
We consider symmetric random walks on discrete, Zariski-dense subgroups of a semisimple Lie group with Property (T). We prove that if has infinite covolume, then the…
Roots of Alexander polynomials of random positive 3-braids
Nathan M. Dunfield, Giulio Tiozzo
Motivated by an observation of Dehornoy, we study the roots of Alexander polynomials of knots and links that are closures of positive 3-strand braids. We give experimental data on…
A cell decomposition for marked cycle curves
Caroline Davis, Malavika Mukundan, Danny Stoll +1
We describe a family of marked cycle curves that parameterize the cycles of period of a given family of dynamical systems. We produc…