Marked random graphs with given degree sequence: large deviations on the local topology and applications
Abstract
We investigate the behavior of the empirical neighborhood distribution of marked graphs in the framework of local weak convergence.Here we extend known results by considering uniform random graphs with given degree sequences and i.i.d.marks on half-edges and vertices.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.Possible applications of these results are in the study of interacting diffusions on top of random graphs.
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Random Matrices and Applications
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- Latin American Journal of Probability and Mathematical Statistics
- Volume
- 23
- Issue
- 1
- Pages
- 83–83
- Publication date
- 1 January 2026
- Language
- EN