This paper discusses a sufficient condition for recurrence of the \(d\)-dimensional stationary random walk defined by a Borel map \(f:X\to R^d\), \(d\geq 1\), in terms of the asymptotic distributions of the maps \((f+fT+ \cdots+ fT^{n-1})/n^{1/d}\), \(n\geq 1\). When \(d=2\), the recurrence of the two-dimensional random walk is obtained as a particular case.