Publications

We investigate the voter model on heterogeneous networks and find that on scale-free networks with degree exponent 2 < gamma < 3, the consensus time is sublinear in the number of nodes, while for gamma > 3 it is linear, as on regular lattices.

Extended study of voter dynamics on artificial scale-free networks and real networks, finding scaling regimes for consensus time that depend on the degree distribution exponent, explained through random walk analysis and the role of network hubs.

We study fixation probability of mutants on graphs under two regulation mechanisms. For the Moran process on any graph, fixation probability equals that of a well-mixed population. For the voter model, it depends on structure via a surprisingly simple expression.

We investigate first-passage times on Erdos-Renyi random graphs using the connection to resistance in analogous resistor networks, finding scaling with N/z above the critical point and N^(2/3) at criticality.

We discover a localization transition at critical bias alpha_c = 1 for random walks on scale-free networks. Above the critical value, the walker localizes around the highest-degree hub; below, it is delocalized across the network.

We analyze the state space of random Boolean networks as a complex network, finding broad distributions with scaling behavior for component sizes, basin sizes, and cycle lengths, suggesting critical dynamics.

We introduce a random sequential renormalization method for networks and apply it to critical trees, obtaining exact results for the renormalization flow and fixed points.