Marked random graphs with given degree sequence: large deviations on the local topology
Probability
2024-01-02 v1
Abstract
We investigate the behavior of the empirical neighbourhood distribution of marked graphs in the framework of local weak convergence. We establish a large deviation principle for such families of empirical measures. The proof builds on Bordenave and Caputo's seminal 2015 paper, and Delgosha and Anantharam's 2019 introduction of BC entropy, relying on combinatorial lemmas that allow one to construct suitable approximations of measures supported on marked trees.
Cite
@article{arxiv.2401.00351,
title = {Marked random graphs with given degree sequence: large deviations on the local topology},
author = {Rangel Baldasso and Alan Pereira and Guilherme Reis},
journal= {arXiv preprint arXiv:2401.00351},
year = {2024}
}