Path-integral approach to the dynamics in sparse random network

TL;DR

This paper extends mean-field theory for sparse random networks using a path-integral approach, showing that the variable distribution matches that of globally coupled oscillators with Gaussian interactions, supported by numerical simulations.

Contribution

It introduces a path-integral method to analyze sparse network dynamics, bridging the gap with globally coupled oscillator models.

Findings

Distribution of variables matches that of Gaussian-coupled oscillators

Numerical simulations confirm the theoretical predictions

The approach enhances understanding of sparse network dynamics

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.