Launay, Claire Galerne, Bruno Desolneux, Agnès

Determinantal point processes (DPPs) enable the modeling of repulsion: they provide diverse sets of points. The repulsion is encoded in a kernel $K$ that can be seen as a matrix storing the similarity between points. The diversity comes from the fact that the inclusion probability of a subset is equal to the determinant of a submatrice of $K$. The ...

Belhadji, Ayoub

Determinantal point processes are probabilistic models of repulsion. These models were studied in various fields: random matrices, quantum optics, spatial statistics, image processing, machine learning, and recently numerical integration. In this thesis, we study subspace sampling using determinantal point processes. This problem takes place within...

Decreusefond, Laurent Moroz, Guillaume

We analyze several optimal transportation problems between de-terminantal point processes. We show how to estimate some of the distances between distributions of DPP they induce. We then apply these results to evaluate the accuracy of a new and fast DPP simulation algorithm. We can now simulate in a reasonable amount of time more than ten thousands...

Poinas, Arnaud

We prove a general inequality on $\beta$-mixing coefficients of point processes depending uniquely on their $n$-th order intensity functions. We apply this inequality in the case of determinantal point processes and show that the rate of decay of the $\beta$-mixing coefficients of a wide class of DPPs is optimal.

Launay, Claire Desolneux, Agnès Galerne, Bruno

Determinantal point processes (DPPs) are probabilistic models of configurations that favour diversity or repulsion. They have recently gained influence in the machine learning community, mainly because of their ability to elegantly and efficiently subsample large sets of data. In this paper, we consider DPPs from an image processing perspective, me...

Berggren, Tomas

This thesis is dedicated to asymptotic analysis of determinantal point processes originating from random matrix theory and random tiling models. Our main interest lies in random tilings of planar domains with doubly periodic weights. Uniformly distributed random tiling models are known to be a very rich class of models where many interesting phenom...

Clarenne, Adrien

In this thesis, we study the asymptotic behavior of random balls models generated by different point processes, after performing a zoom-out on the model. Limit theorems already exist for Poissonian random balls and we generalize the existing results first by studying determinantal random balls models, which induce repulsion between the centers of t...

Kuijlaars, Arno BJ; 17946; Mina-Diaz, Erwin;

status: published

Betea, Dan Bouttier, Jérémie
Published in
Mathematical Physics, Analysis and Geometry

We revisit the periodic Schur process introduced by Borodin in 2007. Our contribution is threefold. First, we provide a new simpler derivation of its correlation functions via the free fermion formalism. In particular, we shall see that the process becomes determinantal by passing to the grand canonical ensemble, which gives a physical explanation ...

Bufetov, Alexander

The main result of this paper is that determinantal point processes on R corresponding to projection operators with integrable kernels are quasiinvariant, in the continuous case, under the group of diffeomorphisms with compact support (Theorem 1.4); in the discrete case, under the group of all finite permutations of the phase space (Theorem 1.6). T...