An integral test for the transience of a brownian path with limited local time
Itai Benjamini, Nathanaël Berestycki (2011)
Annales de l'I.H.P. Probabilités et statistiques
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We study a one-dimensional brownian motion conditioned on a self-repelling behaviour. Given a nondecreasing positive function (), ≥0, consider the measures obtained by conditioning a brownian path so that ≤(), for all ≤, where is the local time spent at the origin by time . It is shown that the measures are tight, and that any weak limit of as →∞ is transient provided that −3/2() is integrable. We conjecture...