Mutually excited random walks

Noam Berger; Eviatar B. Procaccia

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arXiv · 1210.7664

Mutually excited random walks

Noam Berger·Eviatar B. Procaccia

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Abstract

Consider two random walks on $\mathbb{Z}$. The transition probabilities of each walk is dependent on trajectory of the other walker i.e. a drift $p>1/2$ is obtained in a position the other walker visited twice or more. This simple model has a speed which is, according to simulations, not monotone in $p$, without apparent "trap" behaviour. In this paper we prove the process has positive speed for $1/2<p<1$, and present a deterministic algorithm to approximate the speed and show the non-monotonicity.

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Noam Berger, Eviatar B. Procaccia. 2012-10-29. Mutually excited random walks. https://arxiv.org/abs/1210.7664

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