The large deviation principle for interacting dynamical systems on random graphs

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 Erdős-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.

The proof of lower semicontinuity of the rate function was added (see Appendix). The form of the rate function for sparse random graphs was corrected (see Theorem 7.4). A number of smaller changes were made