Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: First passages for a search by a swarm of independent random searchers   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 \{\tau_k\}, where \tau_k is the time of the first
passage of the k-th searcher to the location of the target. Clearly, \tau_k's
are independent, identically distributed random variables with the same
distribution function \Psi(\tau). We evaluate then the distribution P(\omega)
of the random variable \omega \sim \tau_1/bar{\tau}, where bar{\tau} = N^{-1}
\sum_{k=1}^N \tau_k is the ensemble-averaged realization-dependent first
passage time. We show that P(\omega) exhibits quite a non-trivial and sometimes
a counterintuitive behaviour. We demonstrate that in some well-studied cases
e.g., Brownian motion in finite d-dimensional domains) the \textit{mean} first
passage time is not a robust measure of the search efficiency, despite the fact
that \Psi(\tau) has moments of arbitrary order. This implies, in particular,
that even in this simplest case (not saying about complex systems and/or
anomalous diffusion) first passage data extracted from a single particle
tracking should be regarded with an appropriate caution because of the
significant sample-to-sample fluctuations.

18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph