Diffusivity of a random walk on random walks

Emmanuel Boissard (1) , Serge Cohen (1) , Thibault Espinasse (1) , James Norris (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 Statistical Laboratory [Cambridge]

We consider a random walk $\left(Z^{(1)}_n, \cdots, Z^{(K+1)}_n \right) \in \mathbb{Z}^{K+1}$ 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.

Mots clés: Random walk; Graph; Central limit theorem

Domaines: Probabilités [math.PR]

Emmanuel Boissard, Serge Cohen, Thibault Espinasse, James Norris. Diffusivity of a random walk on random walks. 2012. ⟨hal-00742938⟩