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arXiv · 2212.03944

LDP for Inhomogeneous U-Statistics

Sohom Bhattacharya·Nabarun Deb·Sumit Mukherjee
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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.

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BibTeXRIS

Sohom Bhattacharya, Nabarun Deb, Sumit Mukherjee. 2022-12-07. LDP for Inhomogeneous U-Statistics. https://arxiv.org/abs/2212.03944

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