Let \(G\) be a countable group acting by isometries on a metric space \((X, d)\) and let \(\mu\) denote a probability measure on \(G\). A random walk on \(X\) is the process defined by \(Z_n = X_n \dots X_1 o\), where \(o \in X \) is a fixed base point, and \(X_i\) are independent \(\mu\)-distributed random variables. Studying statistical properties of the displacement sequence \(d(Z_n, o)\) 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.