Hyperuniform random measures, transport and rigidity

Fuente: arXiv
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Main Author: Lachièze-Rey, Raphaël
Format: Preprint
Published: 2025
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author Lachièze-Rey, Raphaël
author_facet Lachièze-Rey, Raphaël
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2510_18392
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Hyperuniform random measures, transport and rigidity
Lachièze-Rey, Raphaël
Probability
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.
title Hyperuniform random measures, transport and rigidity
topic Probability
url https://arxiv.org/abs/2510.18392