We prove that for almost all realizations of the Boghosian-Levermore stochastic cellular automaton model the density profile converges, in the scaling limit, to the solution of Burgers' equation. The proof goes via the propagation of chaos and yields tight bounds on the fluctuations. These estimates also yield stability properties of the (smooth) shock front: at long times it remains well defined on a microscopic scale-but its location fluctuates.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics