Let $G$ be a countable group acting by isometries on a metric space $(M, d)$, and let $\mu$ denote a probability measure on $G$. The $\mu$-random walk on $M$ is the random process defined by $$Z_n=X_n \dots X_1 o,$$ where $o \in M$ is a fixed base point, and $X_i$ are independent $\mu$-distributed random variables. Studying statistical properties of the displacement sequence $D_n:= d(Z_n, o)$ has been a topic of current research. In this talk, which is based on a joint work with Amin Bahmanian, Behrang Forghani, and Ilya Gekhtman, I will discuss a central limit theorem for $D_n$ in the case that $M$ is the horospherical product of Gromov hyperbolic spaces.