LDP for Inhomogeneous U-Statistics
Abstract
In this paper we derive a Large Deviation Principle (LDP) for inhomogeneous U/V-statistics of a general order. Using this, we derive a LDP for two types of statistics: random multilinear forms, and number of monochromatic copies of a subgraph. We show that the corresponding rate functions in these cases can be expressed as a variational problem over a suitable space of functions. We use the tools developed to study Gibbs measures with the corresponding Hamiltonians, which include tensor generalizations of both Ising (with non-compact base measure) and Potts models. For these Gibbs measures, we establish scaling limits of log normalizing constants, and weak laws in terms of weak* topology, which are of possible independent interest.
Cite
@article{arxiv.2212.03944,
title = {LDP for Inhomogeneous U-Statistics},
author = {Sohom Bhattacharya and Nabarun Deb and Sumit Mukherjee},
journal= {arXiv preprint arXiv:2212.03944},
year = {2026}
}
Comments
37 pages, accepted for publication in the Annals of Applied Probability