7 papers
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…
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…
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…
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…
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…