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Please use this identifier to cite or link to this item: http://hdl.handle.net/2289/6666
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dc.contributor.authorMajumdar, Satya N.-
dc.contributor.authorSabhapandit, Sanjib-
dc.contributor.authorSchehr, Gregory-
dc.date.accessioned2017-07-04T06:19:58Z-
dc.date.available2017-07-04T06:19:58Z-
dc.date.issued2016-12-
dc.identifier.citationPhysical Review E, 2016, Vol 94, p062131en_US
dc.identifier.issn2470-0053 (Online)-
dc.identifier.issn2470-0045-
dc.identifier.urihttp://hdl.handle.net/2289/6666-
dc.descriptionOpen Accessen_US
dc.description.abstractWe 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.en_US
dc.language.isoenen_US
dc.relation.urihttp://arxiv.org/abs/1609.06325en_US
dc.relation.urihttp://dx.doi.org/10.1103/PhysRevE.94.062131en_US
dc.relation.urihttp://adsabs.harvard.edu/abs/2016PhRvE..94f2131Men_US
dc.rights2016 American Physical Societyen_US
dc.titleExact distributions of cover times for N independent random walkers in one dimensionen_US
dc.typeArticleen_US
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