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Communications in Mathematical Physics

, Volume 104, Issue 3, pp 509–528 | Cite as

Propriétés d'intersection des marches aléatoires

II. Etude des cas critiques
  • J. -F. Le Gall
Article

Abstract

LetI n denote the number of common points to the paths, up to timen, of two independent random walks with values in ℤ4. The sequence (logn)−1I n is shown to converge in distribution towards the square of a normal variable. Limit theorems are also proved for some processes related to the sequence (I n ), which lead to a better understanding of recent results obtained by G.F. Lawler. Similar statements are proved for the paths of three independent random walks with values in ℤ3.

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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • J. -F. Le Gall
    • 1
  1. 1.Laboratoire de ProbabilitésUniversité Pierre et Marie CurieParis Cedex 05France

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