arXiv subjects

André Goldman

Publications and source records attributed to André Goldman.

3 recordsLinked to original sources

arXiv2023

The CS decomposition and conditional negative correlation inequalities for determinantal processes

For a conditional process of the form $(ϕ\vert A_{i} \not\subset ϕ)$ where $ϕ$ is a determinantal process we obtain a new negative correlation inequalities. Our approach relies upon the underlying geometric structure of the elementary discrete determinantal processes by using the canonical representation of a pair of subspaces in terms of principal vectors and angles, as well as the classical CS decomposition.

math.PR↗

arXiv2022

A note related to the CS decomposition and the BK inequality for discrete determinantal processes

We prove that for a discrete determinantal process the BK inequality occurs for increasing events generated by simple points. We give also some elementary, but nonetheless appealing relationship, between a discrete determinantal process and the well-known CS decomposition.

math.PR↗

arXiv2010

The Palm measure and the Voronoi tessellation for the Ginibre process

We prove that the Palm measure of the Ginibre process is obtained by removing a Gaussian distributed point from the process and adding the origin. We obtain also precise formulas describing the law of the typical cell of Ginibre--Voronoi tessellation. We show that near the germs of the cells a more important part of the area is captured in the Ginibre--Voronoi tessellation than in the Poisson--Voronoi tessellation. Moment areas of corresponding subdomains of the cells are explicitly evaluated.

math.PR↗