First passages for a search by a swarm of independent random searchers

By Carlos Mejía-Monasterio, G. Oshanin, G. Schehr. 2011

118 citations recorded by the source corpus.

In this paper we study some aspects of search for an immobile target by a swarm of N non-communicating, randomly moving searchers (numbered by the index k, k = 1, 2,..., N), which all start their random motion simultaneously at the same point in space. For each realization of the search process, we record the unordered set of time moments {τk}, where τk is the time of the first passage of the kth searcher to the location of the target. Clearly, τks are independent, identically distributed random variables with the same distribution function Ψ(τ). We evaluate then the distribution P(ω) of the random variable , where is the ensemble-averaged realization-dependent first passage time. We show that P(ω) exhibits quite a non-trivial and sometimes a counterintuitive behavior. We demonstrate that in some well-studied cases (e.g. Brownian motion in finite d-dimensional domains) the mean first passage time is not a robust measure of the search efficiency, despite the fact that Ψ(τ) has moments of arbitrary order. This implies, in particular, that even in this simplest case (not to mention complex systems and/or anomalous diffusion) first passage data extracted from a single-particle tracking should be regarded with appropriate caution because of the significant sample-to-sample fluctuations.

Subfields: Mathematical Physics, Molecular Biology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ba258a5e1dfc27c4a436effd122d6616f18a699e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. G. Schehr
2. M. Evans
3. Satya N. Majumdar
4. Svante Janson

In Molecular Biology

1. G. Schehr
2. Satya N. Majumdar
3. M. Evans
4. Shamik Gupta
5. A. Jayannavar

In Statistical and Nonlinear Physics

1. Satya N. Majumdar
2. M. Evans
3. G. Schehr
4. Shamik Gupta
5. A. Jayannavar

Citations in the corpus

• Persistence and first-passage properties in nonequilibrium systems (2013, background): “he recent past and a host of exact and approximate analytical results are available. It was also shown that rst-passage time, even in bounded domains, exhibits interesting sample-to-sample uctuations [384, 385]. The mean rst-passage time has also played a central role in analysing search strategies.”
• Stochastic resetting and applications (2019, background): “sonian case where each particle is reset with the same rate r. One may think of a team of searchers seeking a target and the whole process stops when any one of the searchers nds the target (see e.g. [83,101]). We are interested in the survival probability Ps(t) of the target, i.e. the probability t”