• Corpus ID: 247475906

On estimating the structure factor of a point process, with applications to hyperuniformity

  title={On estimating the structure factor of a point process, with applications to hyperuniformity},
  author={Diala Hawat and Guillaume Gautier and R{\'e}mi Bardenet and Raphael Lachi{\`e}ze-Rey},
Hyperuniformity is the study of stationary point processes with a sub-Poisson variance in a large window. In other words, counting the points of a hyperuniform point process that fall in a given large region yields a small-variance Monte Carlo estimation of the volume. Hyperuniform point processes have received a lot of attention in statistical physics, both for the investigation of natural organized structures and the synthesis of materials. Unfortunately, rigorously proving that a point… 



The spectral analysis of two-dimensional point processes

1. BASIC FORMULAE In a previous paper (Bartlett, 1963 b) I have developed in some detail statistical techniques for estimating and analysing the spectrum of a stationary point stochastic process in

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A stable partial matching of the (possibly randomized) $d$-dimensional lattice with a stationary determinantal point process $\Psi$ on $\mathbb{R}^d$ with intensity $\alpha>1$ with hyperuniformity and number rigid properties is studied.

Lecture Notes for EE 261 the Fourier Transform and Its Applications

  • CreateSpace Independent Publishing Platform,
  • 2014

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This article determines how to implement spatial spectral analysis of point processes (in two dimensions or more), by establishing the moments of raw spectral summaries of point processes. We

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This work introduces a simple randomization idea for creating unbiased estimators in such a setting based on a sequence of approximations for computing expectations of path functionals associated with stochastic differential equations (SDEs).

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In this paper, we discuss the properties of a quadrature formula with the zeros of the Bessel functions as nodes for integrals ∞ −∞ |x| 2ν+1 f (x)dx, where ν is a real constant greater than − 1a ndf

Order, fluctuations, rigidities

  • 2021

A nonparametric estimator for pairwise-interaction point processes

SUMMARY The paper develops a nonparametric estimator for the class of pairwise-interaction point processes. The estimator is based on an approximation in statistical physics due to Percus and Yevick,