Brownian motion and random walks on manifolds

Nicolas Th. Varopoulos

Displaying similar documents to “Brownian motion and random walks on manifolds”

Brownian motion and transient groups

Nicolas Th. Varopoulos (1983)

Annales de l'institut Fourier

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In this paper I consider $\tilde{M} \to M$ a covering of a Riemannian manifold $M$ . I prove that Green’s function exists on $\tilde{M}$ if any and only if the symmetric translation invariant random walks on the covering group $G$ are transient (under the assumption that $M$ is compact).

One-dimensional random walks, decreasing rearrangements and discrete Steiner symmetrization

Alexander R. Pruss (1997)

Annales de l'I.H.P. Probabilités et statistiques

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Random walk local time approximated by a brownian sheet combined with an independent brownian motion

Endre Csáki, Miklós Csörgő, Antónia Földes, Pál Révész (2009)

Annales de l'I.H.P. Probabilités et statistiques

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Let (, ) be the local time of a simple symmetric random walk on the line. We give a strong approximation of the centered local time process (, )−(0, ) in terms of a brownian sheet and an independent Wiener process (brownian motion), time changed by an independent brownian local time. Some related results and consequences are also established.

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

N. Enriquez, C. Lucas, F. Simenhaus (2010)

Annales de l'I.H.P. Probabilités et statistiques

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We identify the limit of the internal DLA cluster generated by Sinai’s walk as the law of a functional of a brownian motion which turns out to be a new interpretation of the Arcsine law.

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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