Related papers: Introduction to determinantal point processes from…

In this note, we show that determinantal point processes on the real line corresponding to de Branges spaces of entire functions are rigid in the sense of Ghosh-Peres and, under certain additional assumptions, quasi-invariant under the…

A determinantal point process (DPP) is an ensemble of random nonnegative-integer-valued Radon measures $\Xi$ on a space $S$ with measure $\lambda$, whose correlation functions are all given by determinants specified by an integral kernel…

Given a positive definite, bounded linear operator $A$ on the Hilbert space $\mathcal{H}_0:=l^2(E)$, we consider a reproducing kernel Hilbert space $\mathcal{H}_+$ with a reproducing kernel $A(x,y)$. Here $E$ is any countable set and…

Let "mu" be a point process on a countable discrete space "X". Under assumption that "mu" is quasi-invariant with respect to any finitary permutation of "X", we describe a general scheme for constructing an equilibrium Kawasaki dynamics for…

Consider Dyson's Hermitian Brownian motion model after a finite time S, where the process is started at N equidistant points on the real line. These N points after time S form a determinantal process and has a limit as N tends to infinity.…

Determinantal point processes have arisen in diverse settings in recent years and have been investigated intensively. We study basic combinatorial and probabilistic aspects in the discrete case. Our main results concern relationships with…

Let $X$ be an underlying space with a reference measure $\sigma$. Let $K$ be an integral operator in $L^2(X,\sigma)$ with integral kernel $K(x,y)$. A point process $\mu$ on $X$ is called determinantal with the correlation operator $K$ if…

We consider fermion (or determinantal) random point fields on Euclidean space $\mbR^d$. Given a bounded, translation invariant, and positive definite integral operator $J$ on $L^2(\mbR^d)$, we introduce a determinantal interaction for a…

The $\alpha$-determinant is a one-parameter generalisation of the standard determinant, with $\alpha=-1$ corresponding to the determinant, and $\alpha=1$ corresponding to the permanent. In this paper a simple limit procedure to construct…

Determinantal point processes (DPPs) are repulsive point processes where the interaction between points depends on the determinant of a positive-semi definite matrix. The contributions of this paper are two-fold. First of all, we introduce…

For a broad class of point processes, including determinantal point processes, we construct associated marked and conditional ensembles, which allow to study a random configuration in the point process, based on information about a randomly…

This paper introduces a new idea for constructing operators associated with a certain class of probability measures. Special cases include several know classical and noncommutative probability. The main example is derived from Feller [30,…

Some fifty years ago, in her seminal PhD thesis, Odile Macchi introduced permanental and determinantal point processes. Her initial motivation was to provide models for the set of detection times in fundamental bosonic or fermionic optical…

Motivated by questions in quantum theory, we study Hilbert space valued Gaussian processes, and operator-valued kernels, i.e., kernels taking values in B(H) (= all bounded linear operators in a fixed Hilbert space H). We begin with a…

Statistical models and methods for determinantal point processes (DPPs) seem largely unexplored. We demonstrate that DPPs provide useful models for the description of spatial point pattern datasets where nearby points repel each other. Such…

We show that the central limit theorem for linear statistics over determinantal point processes with $J$-Hermitian kernels holds under fairly general conditions. In particular, We establish Gaussian limit for linear statistics over…

We consider the Bochner-Schr\"odinger operator $H_{p}=\frac 1p\Delta^{L^p}+V$ on tensor powers $L^p$ of a Hermitian line bundle $L$ on a Riemannian manifold $X$ of bounded geometry under the assumption of non-degeneracy of the curvature…

We consider an abstract determinantal point process on a general non--elementary Gromov hyperbolic metric space governed by an orthogonal projection in the case when the space is homogeneous and the point process is invariant under…

We study Palm measures of determinantal point processes with $J$-Hermitian correlation kernels. A point process $\mathbb{P}$ on the punctured real line $\mathbb{R}^* = \mathbb{R}_{+} \sqcup \mathbb{R}_{-}$ is said to be $\textit{balanced…

We consider a new class of determinantal point processes in the complex plane coming from the ground state of free fermions associated with Berezin--Toeplitz operators. These processes generalize the Ginibre ensemble from random matrix…