Keivan Mallahi-Karai (Constructor University) | Central limit theorem for random walks on horospherical products of Gromov hyperbolic spaces

Startdatum: 22.06.2023 - 14:15
Enddatum: 22.06.2023 - 15:45
Adresse: MZH 4140
Preis: 0€

Let G be a countable group acting by isometries on a metric space (X,d) and let μ denote a probability measure on G. A random walk on X is the process defined by Zn = XnX1o, where o ∈ X is a fixed base point, and Xi are independent μ-distributed random variables. Studying statistical properties of the displacement sequence d(Zn,o) has been a topic of current research.

Extending a work of Cartwright-Kaimanovich-Woess, we prove a law of large numbers and a central limit theorem for displacements of random walks on horospherical products of Gromov hyperbolic spaces. In this talk, which is based on a joint work with Amin Bahmanian, Behrang Forghani, and Ilya Gekhtman, I will discuss some of the underlying concepts as well as the key steps of the proof for horospherical products of trees.