Stochastic search with Poisson and deterministic resetting

Abstract

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