  We investigate the evolution of a population of non-interacting particles
which undergo diffusion and multiplication. Diffusion is assumed to be
homogeneous, while multiplication proceeds with different rates reflecting the
distribution of nutrients. We focus on the situation where the distribution of
nutrients is a stationary quenched random variable, and show that the
population exhibits a super-exponential growth whenever the nutrient
distribution is unbounded. We elucidate a huge difference between the average
and typical asymptotic growths and emphasize the role played by the spatial
correlations in the nutrient distribution.
