arXiv subjects

K. Ravishankar

Publications and source records attributed to K. Ravishankar.

20 records · Page 2Linked to original sources

arXiv2002

The Brownian Web

Arratia, and later Tóth and Werner, constructed random processes that formally correspond to coalescing one-dimensional Brownian motions starting from every space-time point. We extend their work by constructing and characterizing what we call the {\em Brownian Web} as a random variable taking values in an appropriate (metric) space whose points are (compact) sets of paths. This leads to general convergence criteria and, in particular, to convergence in distribution of coalescing random walks in the scaling limit to the Brownian Web.

math.PR↗

arXiv2001

The shape theorem for the frog model with random initial configuration

We prove a shape theorem for a growing set of simple random walks on Z^d, known as frog model. The dynamics of this process is described as follows: There are active particles, which perform independent discrete time SRWs, and sleeping particles, which do not move. When a sleeping particle is hit by an active particle, the former becomes active as well. Initially, a random number of particles is placed into each site. At time 0 all particles are sleeping, except for those placed at the origin. We prove that the set of all sites visited by active particles, rescaled by the elapsed time, converges to a compact convex set.

math.PR↗