3 papers
math.PR2026
Hyperuniform random measures, transport and rigidity
Raphaël Lachièze-Rey
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 sta…
math.PR2026
From smooth to discontinuous kernels: a variance transfer principle for hyperuniform processes
Raphaël Lachièze-Rey
We give a transfer principle for the fluctuations of linear statistics of finite particle systems around Lebesgue measure: if for a smooth kernel the variance decays polynomially w…
math.PR2026
Maximal rigidity of random measure and uniqueness pairs: stealthy processes, quasicrystals and periodicity
Raphaël Lachièze-Rey
This article investigates the phenomenon of maximal rigidity in spatial processes, where perfect interpolation of the process is possible from partial information, specifically, fr…