Showing papers by "Enzo Orsingher published in 2008"
TL;DR: In this paper, a random motion on the Poincare half-plane is studied, where a particle runs on the geodesic lines changing direction at Poisson-paced times.
Abstract: A random motion on the Poincare half-plane is studied. A particle runs on the geodesic lines changing direction at Poisson-paced times. The hyperbolic distance is analyzed, also in the case where returns to the starting point are admitted. The main results concern the mean hyperbolic distance (and also the conditional mean distance) in all versions of the motion envisaged. Also an analogous motion on orthogonal circles of the sphere is examined and the evolution of the mean distance from the starting point is investigated.
19 citations
TL;DR: In this article, a branching process of particles moving at finite velocity over the geodesic lines of the hyperbolic space (Poincare halfplane and Poincare disk) is examined.
Abstract: A branching process of particles moving at finite velocity over the geodesic lines of the hyperbolic space (Poincare half-plane and Poincare disk) is examined. Each particle can split into two particles only once at Poisson spaced times and deviates orthogonally when splitted. At time t, after N(t) Poisson events, there are N(t)+1 particles moving along different geodesic lines. We are able to obtain the exact expression of the mean hyperbolic distance of the center of mass of the cloud of particles. We derive such mean hyperbolic distance from two different and independent ways and we study the behavior of the relevant expression as t increases and for different values of the parameters c (hyperbolic velocity of motion) and λ (rate of reproduction). The mean hyperbolic distance of each moving particle is also examined and a useful representation, as the distance of a randomly stopped particle moving over the main geodesic line, is presented.
12 citations
TL;DR: In this article, the authors considered space inhomogeneous random motions of particles on the line and in the plane, and the changes of the movement direction are driven by a Poisson process.
Abstract: Space inhomogeneous random motions of particles on the line and in the plane are considered in the paper. The changes of the movement direction are driven by a Poisson process. The particles are assumed to move according to a finite velocity field that depends on a spatial argument. The explicit distribution of particles is obtained in the paper for the case of dimension 1 in terms of characteristics of the governing equations. In the case of dimension 2, the distribution is obtained if a rectifying diffeomorphism exists.
1 citations