Proliferation assisted transport in a a random environment

We investigate the competition between barrier slowing down and proliferation induced superdiffusion in a model of population dynamics in a random force field. Numerical results in d = 1 suggest that a new intermediate diffusion behaviour appears. We introduce the idea of proliferation assisted barrier crossing and give a Flory-like argument to understand qualitatively this nontrivial diffusive behaviour. A renormalization group analysis close to the critical dimension d(c) = 2 confirms that the random force fixed point is unstable and flows towards an uncontrolled strong coupling regime.