Democracy and the role of minorities in Markov chain models
Abstract:
Many opinion dynamics models and cooperative algorithms over networks like consensus are mathematically rooted on the dynamics of an irreducible Markov chain P on a set of states V. A key object to study the asymptotic behavior is clearly the invariant probability p of P. In this talk we will study the effect on p of non-reversible perturbations performed on P. One example we will consider is when the perturbation corresponds to a minority of nodes behaving in a different way with respect to the majority. While classical perturbation results for Markov chains can not be applied in this context (since perturbation are localized but possibly large), we will present various results which bound the effect of the perturbation on the invariant measure p. In particular, we will study conditions on the network under which ’minority effects’ become negligeable in the large scale limit.