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 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.
Cite
@article{arxiv.2007.13899,
title = {The large deviation principle for interacting dynamical systems on random graphs},
author = {Paul Dupuis and Georgi Medvedev},
journal= {arXiv preprint arXiv:2007.13899},
year = {2021}
}
Comments
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