title: Path-integral approach to dynamics in a sparse random network.
abstract: We study the dynamics involved in a sparse random network model. We extend the standard mean-field approximation for the dynamics of a random network by employing the path-integral approach. The result indicates that the distribution of the variable is essentially identical to that obtained from globally coupled oscillators with random Gaussian interaction. We present the results of a numerical simulation of the Kuramoto transition in a random network, which is found to be consistent with this analysis.
authors.affiliation: Laboratory of Nonlinear Studies and Computation, Research Institute for Electronic Science, Hokkaido University, Sapporo, Hokkaido, Japan. miya@aurora.es.hokudai.ac.jp
authors.forename: Takashi
authors.initials: T
authors.lastname: Ichinomiya