5 papers · 1 filter
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…
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…
Regularization of a stationary point process by a stationary increments perturbation
Loïc Thomassey, Raphaël Lachièze-Rey, Assaf Shapira
We present a novel procedure where a stationary point process is regularized through the convolution with a continuous random field with stationary increments, in the sense that th…
Hyperuniformity and optimal transport of point processes
Raphaël Lachièze-Rey, D. Yogeshwaran
We examine optimal matchings or transport between two stationary random measures. It covers allocation from the Lebesgue measure to a point process and matching a point process to…
Rigidity of random stationary measures and applications to point processes
Raphaël Lachièze-Rey
The {\it number rigidity} of a stationary point process entails that for a bounded set the knowledge of on a.s. determines ; th…