Population growth in random media - II. Wavefront propagation - Greven, Andreas; den Hollander, Frank (Journal of Statistical Physics, 1991)
In this second part of a two-part presentation, we continue with the model introduced in Part I. In this part, the initial configuration has one particle at each site to the left of 0 and no particle elsewhere. The expected number of particles observed at a site moving at speed τ≥ has an exponential growth rate (speed-τ growth rate) that is computed explicitly. The result reveals two characteristic wavefront speeds: τ, the speed of the front of zero growth (rightmost particle), and τ, the speed of the front of maximal growth. The latter speed exhibits a phase transition, changing from zero to positive as the drift in the migration crosses a threshold. The qualitative shape of the growth rate as a function of τ changes as well. In particular, below the threshold there appears a linear piece, which corresponds to the system exhibiting an intermittency effect. © 1991 Plenum Publishing Corporatio
Keywords: population growth; random medium; variational formula; Wave front propagation