LAUSR

We study a random target searching performed by N independent searchers in a d-dimensional domain of a large but finite volume. Considering the two initial distributions of searchers where searchers are either uniformly or point distributed, we estimate the mean time for the first of the searchers to reach the target and refer to it as searching time. The searching time for the uniformly distributed searchers exhibits a universal power-law dependence on N, irrespective of dimensionality and the target-to-domain size ratio. For point-distributed searching, the searching time has a logarithmic dependence on N in the large N limit, while in the small N limit, it shows qualitatively different behaviors depending upon r_{0}, the initial distance of the searchers from a target. We obtain a diagram by comparing the searching times of the two initial distributions in the parameter space (r_{0},N) and therein present the asymptotic lines separating three characteristic regions to explain numerical simulation results.