Hyperuniform random measures, transport and rigidity
Probability
2025-10-22 v1
Abstract
This survey explores the foundational theory and recent developments in the study of hyperuniformity. We present a comprehensive mathematical framework in the context of weakly stationary random measures, emphasizing spectral characterizations and second order asymptotics. Classical examples - including determinantal point processes, Gibbs measures, and zero sets of Gaussian analytic functions - are presented in depth to illustrate core principles. We also highlight recent progress connecting hyperuniformity with optimal transport and rigidity phenomena, pointing to emerging directions in the field.
Cite
@article{arxiv.2510.18392,
title = {Hyperuniform random measures, transport and rigidity},
author = {Raphaël Lachièze-Rey},
journal= {arXiv preprint arXiv:2510.18392},
year = {2025}
}