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Propriétés d'intersection des marches aléatoires

II. Etude des cas critiques

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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)−1 I 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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  1. Laboratoire de Probabilités, Université Pierre et Marie Curie, 4, Place Jussieu, Tour 56, F-75230, Paris Cedex 05, France

    J. -F. Le Gall

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  1. J. -F. Le Gall
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Communicated by J. Fröhlich

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Le Gall, J.F. Propriétés d'intersection des marches aléatoires. Commun.Math. Phys. 104, 509–528 (1986). https://doi.org/10.1007/BF01210953

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