Stochastic Search with Poisson and Deterministic Resetting

Abstract

We investigate a stochastic search process in one, two, and three dimensions in which $N$ diffusing searchers that all start at $x_0$ seek a target at the origin. Each of the searchers is also reset to its starting point, either with rate $r$, or deterministically, with a reset time $T$. In one dimension and for a small number of searchers, the search time and the search cost are minimized at a non-zero optimal reset rate (or time), while for sufficiently large $N$, resetting always hinders the search. In general, a single searcher leads to the minimum search cost in one, two, and three dimensions. When the resetting is deterministic, several unexpected feature arise for $N$ searchers, including the search time being independent of $T$ for $1/T\to 0$ and the search cost being independent of $N$ over a suitable range of $N$. Moreover, deterministic resetting typically leads to a lower search cost than in stochastic resetting.

23 pages, 9 figures, IOP format. Revised version: figure added, introductory text added, references added, and various minor changes incorporated. V3: Final version to appear in JSTAT. A few more references added

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Cited by in corpus (3)

• First Passage Under Restart
• Interacting Brownian Motion with Resetting
• Exact distributions of cover times for $N$ independent random walkers in one dimension