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hal-00004055, version 1

Almost sure estimates for the concentration neighborhood of Sinai's walk

Pierre Andreoletti () 1

Abstract: We consider Sinai's random walk in random environment. We prove that infinitely often (i.o.) the size of the concentration neighborhood of this random walk is almost surely bounded. As an application we get that i.o. the maximal distance between two favorite sites is almost surely bounded.

  • 1:  Laboratoire d'Analyse, Topologie, Probabilités (LATP)
  • CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III
  • Domain : Mathematics/Probability
  • Keywords : Random environment – random walk – Sinai's regime – local time – concentration
 
  • hal-00004055, version 1
  • http://hal.archives-ouvertes.fr/hal-00004055
  • oai:hal.archives-ouvertes.fr:hal-00004055
  • From: Pierre Andreoletti <>
  • Submitted on: Tuesday, 25 January 2005 11:11:15
  • Updated on: Tuesday, 25 January 2005 11:14:15