The Arcsine law as the limit of the internal DLA cluster generated by Sinai’s walk

N. Enriquez; C. Lucas; F. Simenhaus

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A local limit theorem for directed polymers in random media : the continuous and the discrete case

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Perturbed random walks and Brownian motions, and local times.

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An asymptotic result for brownian polymers

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We consider a model of the shape of a growing polymer introduced by Durrett and Rogers ( (1992) 337–349). We prove their conjecture about the asymptotic behavior of the underlying continuous process (corresponding to the location of the end of the polymer at time ) for a particular type of repelling interaction function without compact support.

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Abstracts

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Random walk on a building of type Ãr and brownian motion of the Weyl chamber

Bruno Schapira (2009)

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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...