1103.3722 (Patricia Gonçalves et al.)

Scaling limits of additive functionals of interacting particle systems    [PDF]

Patricia Gonçalves, Milton Jara

Using the renormalization method introduced in \cite{GJ}, we prove what we call the {\em local} Boltzmann-Gibbs principle for conservative, stationary interacting particle systems in dimension $d=1$. As applications of this result, we obtain various scaling limits of additive functionals of particle systems, like the occupation time of a given site or extensive additive fields of the dynamics. As a by-product of these results, we also construct a novel process, related to the stationary solution of the stochastic Burgers equation.

View original: http://arxiv.org/abs/1103.3722