Random walks in a Dirichlet environment.
Renewal series and square-root boundaries for Bessel processes.
An invariance principle for Azéma martingales
Effet d'un bruit blanc sur l'oscillateur harmonique de dimension d
Masse des pointes, temps de retour et enroulements en courbure négative
Soient un groupe discret géométriquement fini d’isométries d’une variété de Hadamard pincée et une pointe de l’orbifold associé . Munissant de sa mesure de Patterson-Sullivan , nous obtenons une estimation asymptotique de la masse d’un petit voisinage horocyclique de , moyennant une hypothèse sur la croissance du sous-groupe parabolique associé à , hypothèse qui est réalisée si est symétrique de rang . Nous en déduisons une estimation asymptotique du temps de retour du flot géodésique...
Aging and quenched localization for one-dimensional random walks in random environment in the sub-ballistic regime
We consider transient one-dimensional random walks in a random environment with zero asymptotic speed. An aging phenomenon involving the generalized Arcsine law is proved using the localization of the walk at the foot of “valleys“ of height . In the quenched setting, we also sharply estimate the distribution of the walk at time .
Stastistic of the winding of geodesics on a Riemann surface with finite area and constant negative curvature.
In this paper we show that the windings of geodesics around the cusps of a Riemann surface of a finite area, behave asymptotically as independent Cauchy variables.
Limit laws for transient random walks in random environment on
We consider transient random walks in random environment on with zero asymptotic speed. A classical result of Kesten, Kozlov and Spitzer says that the hitting time of the level converges in law, after a proper normalization, towards a positive stable law, but they do not obtain a description of its parameter. A different proof of this result is presented, that leads to a complete characterization of this stable law. The case of Dirichlet environment turns out to be remarkably explicit.
Canonical lift and exit law of the fundamental diffusion associated with a kleinian group
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