Title:	Exact distributions of cover times for N independent random walkers in one dimension
Authors:	Majumdar, Satya N. Sabhapandit, Sanjib Schehr, Gregory
Issue Date:	Dec-2016
Citation:	Physical Review E, 2016, Vol 94, p062131
Abstract:	We study the probability density function (PDF) of the cover time tc of a finite interval of size L by N independent one-dimensional Brownian motions, each with diffusion constant D. The cover time tc is the minimum time needed such that each point of the entire interval is visited by at least one of the N walkers. We derive exact results for the full PDF of tc for arbitrary N≥1 for both reflecting and periodic boundary conditions. The PDFs depend explicitly on N and on the boundary conditions. In the limit of large N, we show that tc approaches its average value of ⟨tc⟩≈L2/(16DlnN) with fluctuations vanishing as 1/(lnN)2. We also compute the centered and scaled limiting distributions for large N for both boundary conditions and show that they are given by nontrivial N independent scaling functions.
Description:	Open Access
URI:	http://hdl.handle.net/2289/6666
ISSN:	2470-0053 (Online) 2470-0045
Alternative Location:	http://arxiv.org/abs/1609.06325 http://dx.doi.org/10.1103/PhysRevE.94.062131 http://adsabs.harvard.edu/abs/2016PhRvE..94f2131M
Copyright:	2016 American Physical Society
Appears in Collections:	Research Papers (TP)

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