Attractive coupling of determinantal point processes using nonsymmetric kernels

par Arnaud Poinas (Laboratoire de mathématiques de l'université de Poitiers)

mardi 21 oct. 2025, 11:15 → 12:15 Europe/Paris

Salle K. Johnson (1R3, 1er étage)

Determinantal point processes (or DPPs for short) are a family of point processes used to model repulsive point patterns, i.e. a random set of points that avoids being too close to each others. They are defined by a symmetric function, called their kernel, from which most of their properties are derived (correlations, likelihood, summary statistics, simulation algorithms, etc...). DPPs can also be defined using a non-symmetric kernel but this scenario has been rarely studied since most of the nice usual properties of DPPs needs the kernel symmetry to work.

In this talk, we are going to discuss the properties of these DPPs with generic kernels. First, by taking a look at the necessary and sufficient conditions needed on the kernel for the point process to be well-defined. Then, by generalizing some of the usual properties of DPPs that needs the kernel symmetry. In particular, since DPPs with non-symmetric kernels can generate attraction, we are going to look at how to use them to model marked point patterns with attraction between points of the same mark and repulsion between points of different marks.