The large deviation principle for interacting dynamical systems on random graphs

TL;DR

This paper establishes a large deviation principle for W-random graphs in the cut-norm topology and extends it to interacting dynamical systems, generalizing previous results for Erdős-Rényi graphs using the weak convergence approach.

Contribution

It introduces a generalized LDP for W-random graphs and applies it to dynamical systems, demonstrating continuous dependence on graph structures.

Findings

LDP formulated for W-random graphs in cut-norm topology

Extension of LDP to interacting dynamical systems on these graphs

Demonstration of continuous dependence of solutions on graph structure

Abstract

Using the weak convergence approach to large deviations, we formulate and prove the large deviation principle (LDP) for W-random graphs in the cut-norm topology. This generalizes the LDP for Erd\H{o}s-R{\' e}nyi random graphs by Chatterjee and Varadhan. Furthermore, we translate the LDP for random graphs to a class of interacting dynamical systems on such graphs. To this end, we demonstrate that the solutions of the dynamical models depend continuously on the underlying graphs with respect to the cut-norm and apply the contraction principle.