Related papers: Number rigid determinantal point processes induced…
We discuss several examples of point processes (all taken from Hough, Krishnapur, Peres, Vir\'ag (2009)) for which the autocorrelation and diffraction measures can be calculated explicitly. These include certain classes of determinantal and…
In this paper, we will derive the first and 2nd order Wiener chaos decomposition for the multivariate linear statistics of the determinantal point processes associated with the spectral projection kernels on the unit spheres $S^d$. We will…
We study determinantal random point processes on a compact complex manifold X associated to an Hermitian metric on a line bundle over X and a probability measure on X. Physically, this setup describes a free fermion gas on X subject to a…
We obtain the empirical strong law of large numbers, empirical Glivenko-Cantelli theorem, central limit theorem, functional central limit theorem for various nonparametric Bayesian priors which include the Dirichlet process with general…
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 apply ideas from the theory of limits of dense combinatorial structures to study order types, which are combinatorial encodings of finite point sets. Using flag algebras we obtain new numerical results on the Erd\H{o}s problem of finding…
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…
A 2-dimensional direction-length framework is a collection of points in the plane which are linked by pairwise constraints that fix the direction or length of the line segments joining certain pairs of points. We represent it as a pair…
The point process of vertices of an iteration infinitely divisible or more specifically of an iteration stable random tessellation in the Euclidean plane is considered. We explicitly determine its covariance measure and its pair-correlation…
We study a two-dimensional family of probability measures on infinite Gelfand-Tsetlin schemes induced by a distinguished family of extreme characters of the infinite-dimensional unitary group. These measures are unitary group analogs of the…
When faced with a data set too large to be processed all at once, an obvious solution is to retain only part of it. In practice this takes a wide variety of different forms, and among them "coresets" are especially appealing. A coreset is a…
We study the Borel complexity of sets of normal numbers in several numeration systems. Taking a dynamical point of view, we offer a unified treatment for continued fraction expansions and base $r$ expansions, and their various…
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).
The article investigates high-level general invertible-sequential processing in the digital and quantum domains. In particular it is shown that (i) invertible digital-sequential processes, constructed using a standard general-inversion…
We study Fredholm determinants of a class of integral operators, whose kernels can be expressed as double contour integrals of a special type. Such Fredholm determinants appear in various random matrix and statistical physics models. We…
A finite Borel measure $\mu$ in ${\mathbb R}^d$ is called a frame-spectral measure if it admits an exponential frame (or Fourier frame) for $L^2(\mu)$. It has been conjectured that a frame-spectral measure must be translationally absolutely…
A differential operator $D$ commuting with an $S^1$-action is said to be rigid if the non-constant Fourier coefficients of $\ker D$ and $\coker D$ are the same. Somewhat surprisingly, the study of rigid differential operators turns out to…
We show that given a poset P and and a subposet Q, the integer points obtained by restricting linear extensions of P to Q can be explained via integer lattice points of a generalized permutohedron.
The main result of this paper states that if $(N, \Pi)$ is a pair of independent point processes on a common ground space with $N$ Poisson and $\Pi$ determinantal induced by a locally trace class (not necessarily self-adjoint) correlation…
In this note, we show that extremal Szemer\'{e}di-Trotter configurations are rigid in the following sense: If $P,L$ are sets of points and lines determining at least $C|P|^{2/3}|L|^{2/3}$ incidences, then there exists a collection $P'$ of…