Scale-free percolation mixing time
Scale-free percolation is a spatially inhomogeneous random graph model which features three fundamental properties that are often present in real-world networks: (1) scale-free: the degree of the nodes follows a power law; (2) small-world: two far-away nodes have typically a small graph distance; (3) positive clustering coefficient: two nodes with a common neighbour have a good chance to be linked. We study the mixing time of the simple random walk on this structure in one dimension and depict a rich phase diagram in the parameters of the model, in particular we show that the presence of hubs can speed up the mixing of the chain. Joint work with Michele Salvi (UniversitĂ di Tor Vergata).