Mathematics – Probability
Scientific paper
2011-07-25
J. Stat. Phys., 133, 1137--1159 (2008)
Mathematics
Probability
Scientific paper
A branching process of particles moving at finite velocity over the geodesic lines of the hyperbolic space (Poincar\'e half-plane and Poincar\'e disk) is examined. Each particle can split into two particles only once at Poisson paced 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 $\lambda$ (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.
Cammarota Valentina
Orsingher Enzo
No associations
LandOfFree
Cascades of Particles Moving at Finite Velocity in Hyperbolic Spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Cascades of Particles Moving at Finite Velocity in Hyperbolic Spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cascades of Particles Moving at Finite Velocity in Hyperbolic Spaces will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-572486