University of Miami

**Abstract**: We consider a jump-diffusion process describing a
system of diffusing particles that upon contact with an obstacle (catalyst) die
and are replaced by an independent offspring with position chosen according to
a weighted average of the remaining particles.

Since the mass is conserved, we prove a hydrodynamic limit for the empirical measures, described by a generalized reaction-diffusion equation, asymptotic behavior of the tagged particles including propagation of chaos under mass-preserving scaling in both the case of soft and hard obstacles (catalysts). In the soft obstacle case we provide a large deviations principle from the deterministic hydrodynamic limit.