Determinantal point processes in the flat limit - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Bernoulli Année : 2023

Determinantal point processes in the flat limit

Résumé

Determinantal point processes (DPPs) are repulsive point processes where the interaction between points depends on the determinant of a positive-semi definite matrix. In this paper, we study the limiting process of L-ensembles based on kernel matrices, when the kernel function becomes flat (so that every point interacts with every other point, in a sense). We show that these limiting processes are best described in the formalism of extended L-ensembles and partial projection DPPs, and the exact limit depends mostly on the smoothness of the kernel function. In some cases, the limiting process is even universal, meaning that it does not depend on specifics of the kernel function, but only on its degree of smoothness. Since flat-limit DPPs are still repulsive processes, this implies that practically useful families of DPPs exist that do not require a spatial length-scale parameter.

Dates et versions

hal-03359889 , version 1 (30-09-2021)

Identifiants

Citer

Simon Barthelme, Nicolas Tremblay, Konstantin Usevich, Pierre-Olivier Amblard. Determinantal point processes in the flat limit. Bernoulli, 2023, 29 (2), pp.957-983. ⟨10.48550/arXiv.2107.07213⟩. ⟨hal-03359889⟩
81 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More