100, rue des maths 38610 Gières / GPS : 45.193055, 5.772076 / Directeur : Louis Funar

Jean-François Coeurjolly

Monte-Carlo integration, projections and hyperuniformity
Mardi, 24 Octobre, 2023 - 14:30 à 15:30
Résumé : 

A problem often encountered in the area of computer experiments consists in generating a single space-filling design, say in $W^d$ ($d\ge 1$) where $W$ is a bounded domain of $\mathbb{R}$, in order to achieve multiple tasks, like for instance estimating integrals of the form $\int_{W^\ell} h(x)\mathrm{d}x$ for any $\ell=1,...d$ and any function $h:\mathbb{R}^\ell \to \mathbb{R}$. In the first part, I will show the interest of using repulsive spatial point processes and in particular determinantal point processes to achieve such a task when minimal assumptions on the regularity of integrands are required. In a second and more exploratory part, I will discuss spectral aspects of a spatial point process which are captured by what is called the Bartlett spectrum or more commonly the structure factor. In particular, I will present a few more or less known facts about this function and its links with Monte-Carlo integration and the concept of hyperuniformity.

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