We consider the motion of a particle along the geodesic lines of the Poincaré halfplane. The particle is specularly reflected when it hits randomly-distributed obstacles that are assumed to be motionless. This is the hyperbolic version of the well-known Lorentz Process studied in the Euclidean context. We analyse the limit in which the density of the obstacles increases to infinity and the size of each obstacle vanishes: under a suitable scaling, we prove that our process converges to a Markovian process, namely a random flight on the hyperbolic manifold.
Motion among random obstacles on a hyperbolic space / Orsingher, Enzo; Ricciuti, Costantino; Sisti, Francesco. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - STAMPA. - (2016).
Motion among random obstacles on a hyperbolic space
ORSINGHER, Enzo;RICCIUTI, COSTANTINO;SISTI, FRANCESCO
2016
Abstract
We consider the motion of a particle along the geodesic lines of the Poincaré halfplane. The particle is specularly reflected when it hits randomly-distributed obstacles that are assumed to be motionless. This is the hyperbolic version of the well-known Lorentz Process studied in the Euclidean context. We analyse the limit in which the density of the obstacles increases to infinity and the size of each obstacle vanishes: under a suitable scaling, we prove that our process converges to a Markovian process, namely a random flight on the hyperbolic manifold.File | Dimensione | Formato | |
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