  We consider a random walk $(Z^{(1)}_n, ..., Z^{(K+1)}_n) \in
\mathbb{Z}^{K+1}$ with the constraint that each coordinate of the walk is at
distance one from the following one. In this paper, we show that this random
walk is slowed down by a variance factor $\sigma_K^2 = \frac{2}{K+2}$ with
respect to the case of the classical simple random walk without constraint.
