相关论文: Determinantal random point fields

We give a probabilistic introduction to determinantal and permanental point processes. Determinantal processes arise in physics (fermions, eigenvalues of random matrices) and in combinatorics (nonintersecting paths, random spanning trees).…

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 study the Bergman determinantal point process from a theoretical point of view motivated by its simulation. We construct restricted and restricted-truncated variants of the Bergman kernel and show optimal transport inequalities involving…

We study translation-invariant determinantal random point fields on the real line. We prove, under quite general conditions, that the smallest nearest spacings between the particles in a large interval have Poisson statistics as the length…

As well as arising naturally in the study of non-intersecting random paths, random spanning trees, and eigenvalues of random matrices, determinantal point processes (sometimes also called fermionic point processes) are relatively easy to…

We prove the Central Limit Theorem for the number of eigenvalues near the spectrum edge for hermitian ensembles of random matrices. To derive our results, we use a general theorem, essentially due to Costin and Lebowitz, concerning the…

In this note we present new examples of determinantal point processes with infinitely many particles. The particles live on the half-lattice {1,2,...} or on the open half-line (0,+\infty). The main result is the computation of the…

We present a solution to a problem suggested by Philippe Biane: We prove that a certain Plancherel-type probability distribution on partitions converges, as partitions get large, to a new determinantal random point process on the set…

We prove a local central limit theorem (LCLT) for the number of points $N(J)$ in a region $J$ in $\mathbb R^d$ specified by a determinantal point process with an Hermitian kernel. The only assumption is that the variance of $N(J)$ tends to…

We prove a central limit theorem for a random field generated by d commuting probability preserving transformations; the martingale is given by a commuting filtration (cf. D. Khosnevisan, Multiparameter Processes, Springer 2002). The result…

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…

In this article, recent results about point processes are used in sampling theory. Precisely, we define and study a new class of sampling designs: determinantal sampling designs. The law of such designs is known, and there exists a simple…

We develop a coordinate-free probabilistic framework for determinantal point processes associated with Bergman kernels on compact complex manifolds. The basic issue is that Bergman kernels are naturally line-bundle-valued:…

Tracy and Widom showed that fundamentally important kernels in random matrix theory arise from differential equations with rational coefficients. More generally, this paper considers symmetric Hamiltonian systems abd determines the…

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…

We prove that under fairly general conditions properly rescaled determinantal random point field converges to a generalized Gaussian random process.

In this paper we show that the limiting distribution of the real and the imaginary part of the double Fourier transform of a stationary random field is almost surely an independent vector with Gaussian marginal distributions, whose variance…

Stationary determinantal point processes are proved to be Brillinger mixing. This property is an important step towards asymptotic statistics for these processes. As an important example, a central limit theorem for a wide class of…

In this short note, we extend to the continuous case a mean projection theorem for discrete determinantal point processes associated with a finite range projection, thus strengthening a known result in random linear algebra due to Ermakov…

We study Pfaffian random point fields by using the Moore-Dyson quaternion determinants. First, we give sufficient conditions that ensure that a self-dual quaternion kernel defines a valid random point field, and then we prove a CLT for…