Related papers: Particle-hole transformation in the continuum and …

Let X be a locally compact Polish space and let m be a reference Radon measure on X. Let $\Gamma_X$ denote the configuration space over X, that is, the space of all locally finite subsets of X. A point process on X is a probability measure…

Determinantal point processes are characterized by a special structural property of the correlation functions: they are given by minors of a correlation kernel. However, unlike the correlation functions themselves, this kernel is not…

We study the hole probabilities for ${\mathcal X}_{\infty}^{(\alpha)}$ ($\alpha>0$), a determinantal point process in the complex plane with the kernel $\mathbb…

Determinantal and permanental processes are point processes with a correlation function given by a determinant or a permanent. Their atoms exhibit mutual attraction of repulsion, thus these processes are very far from the uncorrelated…

Let $X$ be a locally compact Polish space and $\sigma$ a nonatomic reference measure on $X$ (typically $X=\mathbb R^d$ and $\sigma$ is the Lebesgue measure). Let $X^2\ni(x,y)\mapsto\mathbb K(x,y)\in\mathbb C^{2\times 2}$ be a $2\times…

The paper is devoted to the study of configuration space analysis by using the projective spectral theorem. For a manifold $X$, let $\Gamma_X$, resp.\ $\Gamma_{X,0}$ denote the space of all, resp. finite configurations in $X$. The so-called…

Let $X$ be a locally compact, second countable Hausdorff topological space. We consider a family of commuting Hermitian operators $a(\Delta)$ indexed by all measurable, relatively compact sets $\Delta$ in $X$ (a quantum stochastic process…

We consider determinantal point processes on a compact complex manifold X in the limit of many particles. The correlation kernels of the processes are the Bergman kernels associated to a a high power of a given Hermitian holomorphic line…

The term "particle-hole symmetry" is beset with conflicting meanings in contemporary physics. Conceived and written from a condensed-matter standpoint, the present paper aims to clarify and sharpen the terminology. In that vein, we propose…

Determinantal point processes on a measure space X whose kernels represent trace class Hermitian operators on L^2(X) are associated to "quasifree" density operators on the Fock space over L^2(X).

In this paper, we study the full asymptotic expansion of the partition functions of determinantal point processes defined on a polarized K\"ahler manifold. We show that the coefficients of the expansion are given by geometric functionals on…

Introduced by Okounkov and Reshetikhin, the Schur process is known to be a determinantal point process, meaning that its correlation functions are minors of a single correlation kernel matrix. Previously, this was derived using…

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…

The commutation relation $KL = LK$ between finite convolution integral operator $K$ and differential operator $L$ has implications for spectral properties of $K$. We characterize all operators $K$ admitting this commutation relation. Our…

The main result of this paper is that determinantal point processes on the real line corresponding to projection operators with integrable kernels are quasi-invariant, in the continuous case, under the group of diffeomorphisms with compact…

In this review paper, we demonstrate that several classes of point processes in a locally compact Polish space $X$ appear as the joint spectral measure of a rigorously defined particle density of a representation of the canonical…

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…

A determinantal point process is a stochastic point process that is commonly used to capture negative correlations. It has become increasingly popular in machine learning in recent years. Sampling a determinantal point process however…

A determinantal point process (DPP) is an ensemble of random nonnegative-integer-valued Radon measures, whose correlation functions are all given by determinants specified by an integral kernel called the correlation kernel. First we show…

Determinantal point processes are point processes whose correlation functions are given by determinants of matrices. The entries of these matrices are given by one fixed function of two variables, which is called the kernel of the point…