English

Diffusivity of a random walk on random walks

Probability 2012-10-18 v1

Abstract

We consider a random walk (Zn(1),...,Zn(K+1))ZK+1(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 σK2=2K+2\sigma_K^2 = \frac{2}{K+2} with respect to the case of the classical simple random walk without constraint.

Keywords

Cite

@article{arxiv.1210.4745,
  title  = {Diffusivity of a random walk on random walks},
  author = {Emmanuel Boissard and Serge Cohen and Thibault Espinasse and James Norris},
  journal= {arXiv preprint arXiv:1210.4745},
  year   = {2012}
}
R2 v1 2026-06-21T22:23:20.009Z