Scaling limits for lattice gas models. (English) Zbl 0884.60090

Goldstein, Jerome A. (ed.) et al., Stochastic processes and functional analysis. In celebration of M. M. Rao’s 65th birthday. Proceedings of the conference, Riverside, CA, USA, November 18–20, 1994. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 186, 39-43 (1997).
This is a popularized talk on the hydrodynamic limits for interacting particle systems. The authors begin with a typical model – the exclusion processes, then deduce nonlinear a partial differential equation that controls the evolution of the density of the particles at time \(t\). Finally, the authors describe a way to determine the diffusion matrix by using a variational formula.
For the entire collection see [Zbl 0856.00029].


60K35 Interacting random processes; statistical mechanics type models; percolation theory