Stochastic Search with Poisson and Deterministic Resetting


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 $1/T\rightarrow 0$ 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.

J. Stat. Mech. 083401 (2016)
Caterina De Bacco
Caterina De Bacco
CyberValley Research Group Leader

My research focuses on understanding, optimizing and predicting relations between the microscopic and macroscopic properties of complex large-scale interacting systems.