Front propagation in an exclusion one-dimensional reactive dynamics

Details Front propagation in an exclusion one-dimensional reactive dynamics Front propagation in an exclusion one-dimensional reactive dynamics

2007-03-06

arxiv.org/abs/math/0703173v1

Mathematics

Probability

19 pages

Scientific paper

We consider an exclusion process representing a reactive dynamics of a pulled front on the integer lattice, describing the dynamics of first class $X$ particles moving as a simple symmetric exclusion process, and static second class $Y$ particles. When an $X$ particle jumps to a site with a $Y$ particle, their position is intechanged and the $Y$ particle becomes an $X$ one. Initially, there is an arbitrary configuration of $X$ particles at sites $..., -1,0$, and $Y$ particles only at sites $1,2,...$, with a product Bernoulli law of parameter $\rho,0<\rho<1$. We prove a law of large numbers and a central limit theorem for the front defined by the right-most visited site of the $X$ particles at time $t$. These results corroborate Monte-Carlo simulations performed in a similar context. We also prove that the law of the $X$ particles as seen from the front converges to a unique invariant measure. The proofs use regeneration times: we present a direct way to define them within this context.

Affiliated with

Also associated with

No associations

Rating

Front propagation in an exclusion one-dimensional reactive dynamics 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 Front propagation in an exclusion one-dimensional reactive dynamics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Front propagation in an exclusion one-dimensional reactive dynamics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-235230