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.
This is a weekly series of informal talks given primarily by members of the soft condensed matter and statistical mechanics groups, but is also open to members of other groups and external visitors. The aim of the series is to promote discussion and learning of various topics at a level suitable to the broad background of the group. Everyone is welcome to attend..