Ordering by random copying on complex networks

Stochastic copying processes, in which individuals in a population are replaced by offspring of parents sampled at random, have been used to model fluctuations in the frequencies of (amongst other things) genes, species, linguistic usages and baby names. They even appear in physics as models of ordering in the absence of surface tension. Having conquered systems with simple spatial structure - regular lattices and the 'mean-field' case of no structure at all - physicists have recently examined complex network structures. A remarkable feature of many such studies is that the 'mean-field' description seems to work rather well for networks too. In this talk I shall attempt to elucidate the explanation for this phenomenon: the 'mean-field' description is exact when there is a separation of emergent timescales within a two-particle reaction-diffusion process defined on the network.