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arXiv · 1210.4745

Diffusivity of a random walk on random walks

Emmanuel Boissard·Serge Cohen·Thibault Espinasse·James Norris
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Abstract

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 $σ_K^2 = \frac{2}{K+2}$ with respect to the case of the classical simple random walk without constraint.

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Emmanuel Boissard, Serge Cohen, Thibault Espinasse, James Norris. 2012-10-17. Diffusivity of a random walk on random walks. https://arxiv.org/abs/1210.4745

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