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Population dynamics in a random environment

Irene Giardina·Jean-Philippe Bouchaud·Marc Mezard
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Abstract

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 non trivial diffusive behaviour. A one loop RG 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.

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Irene Giardina, Jean-Philippe Bouchaud, Marc Mezard. 2000-07-12. Population dynamics in a random environment. https://arxiv.org/abs/cond-mat/0005187

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