704 citations · 2.4k across the 64 of their papers we have counts for
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Random walks of infinite moment on free semigroups
Behrang Forghani, Giulio Tiozzo
We consider random walks on finitely or countably generated free semigroups, and identify their Poisson boundaries for classes of measures which fail to meet the classical entropy…
Counting problems in graph products and relatively hyperbolic groups
Ilya Gekhtman, Samuel J. Taylor, Giulio Tiozzo
We study properties of generic elements of groups of isometries of hyperbolic spaces. Under general combinatorial conditions, we prove that loxodromic elements are generic (i.e. th…
The local Hoelder exponent for the entropy of real unimodal maps
Giulio Tiozzo
We prove that the topological entropy of real unimodal maps depends as a Hoelder continuous function of the kneading parameter, and the local Hoelder exponent equals, up to a facto…
The core entropy for polynomials of higher degree
Yan Gao, Giulio Tiozzo
As defined by W. Thurston, the core entropy of a polynomial is the entropy of the restriction to its Hubbard tree. For each d >= 2, we study the core entropy as a function on the p…