title: Blind and myopic ants in heterogeneous networks.
abstract: The diffusion processes on complex networks may be described by different Laplacian matrices due to heterogeneous connectivity. Here we investigate the random walks of blind ants and myopic ants on heterogeneous networks: While a myopic ant hops to a neighbor node every step, a blind ant may stay or hop with probabilities that depend on node connectivity. By analyzing the trajectories of blind ants, we show that the asymptotic behaviors of both random walks are related by rescaling time and probability with node connectivity. Using this result, we show how the small eigenvalues of the Laplacian matrices generating the two random walks are related. As an application, we show how the return-to-origin probability of a myopic ant can be used to compute the scaling behaviors of the Edwards-Wilkinson model, a representative model of load balancing on networks.
authors.affiliation: Institute for Theoretical Physics, University of Cologne, 50937 Köln, Germany and Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea.
authors.forename: S
authors.initials: S
authors.lastname: Hwang
authors.affiliation: Department of Physics and Department of Natural Medical Sciences, Inha University, Incheon 402-751, Korea.
authors.forename: D-S
authors.initials: DS
authors.lastname: Lee
authors.affiliation: Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea.
authors.forename: B
authors.initials: B
authors.lastname: Kahng