A local limit theorem for directed polymers in random media : the continuous and the discrete case
Vincent Vargas (2006)
Annales de l'I.H.P. Probabilités et statistiques
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Vincent Vargas (2006)
Annales de l'I.H.P. Probabilités et statistiques
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Bruno Schapira (2009)
Annales de l'I.H.P. Probabilités et statistiques
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In this paper we study a random walk on an affine building of type , whose radial part, when suitably normalized, converges toward the brownian motion of the Weyl chamber. This gives a new discrete approximation of this process, alternative to the one of Biane ( (1991) 117–129). This extends also the link at the probabilistic level between riemannian symmetric spaces of the noncompact type and their discrete counterpart, which had been previously discovered...
Jean-François Le Gall, Mathilde Weill (2006)
Annales de l'I.H.P. Probabilités et statistiques
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C. M. Newman, K. Ravishankar, E. Schertzer (2010)
Annales de l'I.H.P. Probabilités et statistiques
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The brownian web (BW), which developed from the work of Arratia and then Tóth and Werner, is a random collection of paths (with specified starting points) in one plus one dimensional space–time that arises as the scaling limit of the discrete web (DW) of coalescing simple random walks. Two recently introduced extensions of the BW, the brownian net (BN) constructed by Sun and Swart, and the dynamical brownian web (DyBW) proposed by Howitt and Warren, are (or should be) scaling limits...
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...