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Greedy walk on the real line
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Foss, Sergey, Rolla, Leonardo T. and Sidoravicius, Vladas (2015) Greedy walk on the real line. The Annals of Probability, 43 (3). pp. 1399-1418. doi:10.1214/13-AOP898 ISSN 0091-1798.
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Official URL: http://dx.doi.org/10.1214/13-AOP898
Abstract
We consider a self-interacting process described in terms of a single-server system with service stations at each point of the real line. The customer arrivals are given by a Poisson point processes on the space–time half plane. The server adopts a greedy routing mechanism, traveling toward the nearest customer, and ignoring new arrivals while in transit. We study the trajectories of the server and show that its asymptotic position diverges logarithmically in time.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||
| Journal or Publication Title: | The Annals of Probability | ||||||
| Publisher: | Institute of Mathematical Statistics | ||||||
| ISSN: | 0091-1798 | ||||||
| Official Date: | 2015 | ||||||
| Dates: |
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| Volume: | 43 | ||||||
| Number: | 3 | ||||||
| Page Range: | pp. 1399-1418 | ||||||
| DOI: | 10.1214/13-AOP898 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access |
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