Related papers: Determinantal point processes and fermions on comp…

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 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 define multideterminantal probability measures, a family of probability measures on $[k]^n$ where $[k]=\{1,2,\dots,k\}$, generalizing determinantal measures (which correspond to the case $k=2$). We give examples coming from the positive…

We introduce and study a 2-parameter family of unitarily invariant probability measures on the space of infinite Hermitian matrices. We show that the decomposition of a measure from this family on ergodic components is described by a…

Let $L$ be a holomorphic line bundle on a compact complex manifold $X$ of dimension $n,$ and let $e^{-\phi}$ be a continuous metric on $L.$ Fixing a measure $d\mu$ on $X$ gives a sequence of Hilbert spaces consisting of holomorphic sections…

It has been shown recently [10] that Cauchy transforms of orthogonal polynomials appear naturally in general correlation functions containing ratios of characteristic polynomials of random NxN Hermitian matrices. Our main goal is to…

We consider an ensemble of non-Hermitian matrices with independent identically distributed real entries that have finite moments. We show that its $k$-point correlation function in the bulk away from the real line converges to a universal…

We prove a central limit theorem for smooth linear statistics associated with zero divisors of standard Gaussian holomorphic sections in a sequence of holomorphic line bundles with Hermitian metrics of class $\mathscr{C}^{3}$ over a compact…

We study the asymptotics of certain measures on partitions (the so-called z-measures and their relatives) in two different regimes: near the diagonal of the corresponding Young diagram and in the intermediate zone between the diagonal and…

Let $X$ be a compact hyperbolic Riemann surface equipped with the Poincar\'e metric. For any integer $k\geq 2$, we investigate the Bergman kernel associated to the holomorphic Hermitian line bundle $\Omega^{\otimes k}_X$, where $\O$ is the…

We study local asymptotics for the spectral projector associated to a Schr\"odinger operator $-\hbar^2\Delta+V$ on $\mathbb{R}^n$ in the semiclassical limit as $\hbar\to0$. We prove local uniform convergence of the rescaled integral kernel…

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 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 prove that general correlation functions of both ratios and products of characteristic polynomials of Hermitian random matrices are governed by integrable kernels of three different types: a) those constructed from orthogonal…

Let L be a positive line bundle on a projective complex manifold. We study the asymptotic behavior of Bergman kernels associated with the tensor powers L^p of L as p tends to infinity. The emphasis is the dependence of the uniform estimates…

We give natural constructions of number rigid determinantal point processes on the unit disc $\mathbb{D}$ with sub-Bergman kernels of the form \[ K_\Lambda(z, w) = \sum_{n\in \Lambda}(n+1) z^n \bar{w}^n, \quad z, w \in \mathbb{D}, \] with…

We consider random analytic functions defined on the unit disk of the complex plane as power series such that the coefficients are i.i.d., complex valued random variables, with mean zero and unit variance. For the case of complex Gaussian…

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…

Determinantal point processes (DPPs) are repulsive point processes where the interaction between points depends on the determinant of a positive-semi definite matrix. In this paper, we study the limiting process of L-ensembles based on…

The paper contains an exposition of recent as well as old enough results on determinantal random point fields. We start with some general theorems including the proofs of the necessary and sufficient condition for the existence of the…