The shadow principle: An optimal survival strategy for a prey chased by random predators

M. Moreau, O. Bénichou, G. Oshanin and R. Voituriez

Physica A: Statistical Mechanics and its Applications, 2013, vol. 392, issue 13, 2837-2846

Abstract: We consider a lattice model of the annihilation process A+B→B, when a mobile prey A is chased by identical, independent predators B performing random motions until one of them finds A and destroys it. It is assumed that each predator follows some “most probable” trajectory around which it performs a random motion. It is shown that, if the random motion of the predators satisfies certain conditions, the prey A can maximize its survival probability by following a specific trajectory which mimics the preferred trajectories of the predators: we call this optimal trajectory as the “shadow” of the predator. This is an extension of the so-called “Pascal Principle”, studied in the recent literature. We discuss the conditions which allow for such extensions, and give examples where they are realized.

Keywords: Random walks; Annihilation process; Survival probability; Pascal principle (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:392:y:2013:i:13:p:2837-2846

DOI: 10.1016/j.physa.2013.02.020

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