24 citations · 67 across the 26 of their papers we have counts for
32 papers
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…
Soohak: A Mathematician-Curated Benchmark for Evaluating Research-level Math Capabilities of LLMs
Guijin Son, Seungone Kim, Catherine Arnett +73
Following the recent achievement of gold-medal performance on the IMO by frontier LLMs, the community is searching for the next meaningful and challenging target for measuring LLM…
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…
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…
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…
Repelled point processes with application to numerical integration
Diala Hawat, Gabriel Mastrilli, Rémi Bardenet +1
We look at Monte Carlo numerical integration from a stochastic geometry point of view. While crude Monte Carlo estimators relate to linear statistics of a homogeneous Poisson point…