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 Z_n = X_n…X₁o, where o ∈ X is a fixed base point, and X_i are independent μ-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.