Random walk through a fertile site
Random walk through a fertile site
We study the dynamics of random walks hopping on homogeneous hypercubic lattices and multiplying at a fertile site. In one and two dimensions, the total number $\mathcal{N}(t)$ of walkers grows exponentially at a Malthusian rate depending on the dimensionality and the multiplication rate $\ensuremath{\mu}$ at the fertile site. When $d>{d}_{c}=2$, …