# Lattice gases with a point source (abstract)

We study diffusive lattice gases with local injection of particles,
namely we assume that whenever the origin becomes empty, a new
particle is immediately injected into the origin. We consider two
lattice gases: a symmetric simple exclusion process and random
walkers. The interplay between the injection events and the positions
of the particles already present implies an effective collective
interaction even for the ostensibly non-interacting random walkers. We
determine the average total number of particles entering into the
initially empty system. We also compute the average total number of
distinct sites visited by all particles, and discuss the shape of the
visited domain and the statistics of visits.