Ordered random walks with heavy tails

Denis Denisov, Vitali Wachtel

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    This paper continues our previous work [4] where we have constructed a k-dimensio-nal random walk conditioned to stay in the Weyl chamber of type A. The construction was done under the assumption that the original random walk has k - 1 moments. In this note we continue the study of killed random walks in the Weyl chamber, and assume that the tail of increments is regularly varying of index α <k-1. It appears that the asymptotic behaviour of random walks is different in this case. We determine the asymptotic behaviour of the exit time, and, using this information, construct a conditioned process which lives on a partial compactification of the Weyl chamber.
    Original languageEnglish
    JournalElectronic Journal of Probability
    Publication statusPublished - 2012


    • Doob h-transform
    • Dyson's brownian motion
    • Martin boundary
    • Superharmonic function
    • Weyl chamber


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