Greedy walk on the real line

• Foss, Sergey ^[1] ; Rolla, Leonardo T ^[2] ; Sidoravicius, Vladas ^[3]
  1. [1] Heriot-Watt University

     Heriot-Watt University

     Reino Unido

     
  2. [2] Univerdidad de Buenos Aires
  3. [3] Instituto de Matemática Pura e Aplicada

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• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 43, Nº. 3, 2015, págs. 1399-1418
• Idioma: inglés
• DOI: 10.1214/13-AOP898
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• Resumen

  • 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.