LDP for Tensor Forms
Abstract
In this paper, we study the large deviation principle (LDP) for a tensor-weighted functional of i.i.d. random variables, when the sequence of tensors converges under a variant of the "bad" cut norm. Using the LDP, we analyze a Gibbs measure with a tensor-valued Hamiltonian, and characterize the optimizers of the limiting variational problem in terms of a functional fixed point equation. As applications, we focus on several concrete examples, which include monochromatic subgraph counts in sparse random graphs, Erdős-Rényi hypergraphs, and a generalized Potts statistic of order v≥ 2. Studying the optimization problem, we give sufficient conditions for uniqueness of the optimizer, as well as for existence of constant optimizers (replica symmetry). Our results demonstrate universal weak laws for a large class of tensor Gibbs models with approximately regular tensors.
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BibTeX
@misc{malekian2026tensor,
title = {{LDP for Tensor Forms}},
author = {Reihaneh Malekian and Sohom Bhattacharya and Nabarun Deb and Sumit Mukherjee},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02682},
eprint = {2609.02682},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02682},
}
RIS
TY - UNPB
TI - LDP for Tensor Forms
AU - Reihaneh Malekian
AU - Sohom Bhattacharya
AU - Nabarun Deb
AU - Sumit Mukherjee
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02682
UR - https://arxiv.org/abs/2609.02682
AB - In this paper, we study the large deviation principle (LDP) for a tensor-weighted functional of i.i.d. random variables, when the sequence of tensors converges under a variant of the "bad" cut norm. Using the LDP, we analyze a Gibbs measure with a tensor-valued Hamiltonian, and characterize the optimizers of the limiting variational problem in terms of a functional fixed point equation. As applications, we focus on several concrete examples, which include monochromatic subgraph counts in sparse random graphs, Erdős-Rényi hypergraphs, and a generalized Potts statistic of order v≥ 2. Studying the optimization problem, we give sufficient conditions for uniqueness of the optimizer, as well as for existence of constant optimizers (replica symmetry). Our results demonstrate universal weak laws for a large class of tensor Gibbs models with approximately regular tensors.
ER -