Optimal transport between determinantal point processes and application to fast simulation

Decreusefond, Laurent; Moroz, Guillaume

doi:10.15559/21-VMSTA180

Modern Stochastics: Theory and Applications

Optimal transport between determinantal point processes and application to fast simulation

Volume 8, Issue 2 (2021), pp. 209–237

Laurent Decreusefond ¹

Guillaume Moroz ¹

https://doi.org/10.15559/21-VMSTA180

Pub. online: 2 June 2021 Type: Research Article

Open Access

¹ Supported by grant ANR-17-CE40-0017 of the French National Research Agency (ANR project ASPAG). The authors are indebted to the anonymous referees for their very insightful remarks which helped them to improve this paper.

Received
1 November 2020

Revised
1 April 2021

Accepted
10 May 2021

Published
2 June 2021

Abstract

Two optimal transport problems between determinantal point processes (DPP for short) are investigated. It is shown how to estimate the Kantorovitch–Rubinstein and Wasserstein-2 distances between distributions of DPP. These results are applied to evaluate the accuracy of a fast but approximate simulation algorithm of the Ginibre point process restricted to a circle. One can now simulate in a reasonable amount of time more than ten thousands points.

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