Related papers: Rigidity of determinantal point processes on the u…

In this note we study a natural measure on plane partitions giving rise to a certain discrete-time Muttalib-Borodin process (MBP): each time-slice is a discrete version of a Muttalib-Borodin ensemble (MBE). The process is determinantal with…

We study determinantal point processes (DPP) through the lens of algebraic statistics. We count the critical points of the log-likelihood function, and we compute them for small models, thereby disproving a conjecture of Brunel, Moitra,…

We prove the stochastic domination for determinantal processes associated with finite rank projection kernels. The result was first proved by Lyons in discrete setting. We avoid the machinery of matroids in order to obtain a proof that…

We investigate different geometrical properties of the inhomogeneous Poisson point process $\Lambda_{\mu}$ associated to a positive, locally finite, $\sigma$-finite measure $\mu$ on the unit disk. In particular, we characterize the…

In this paper, we develop the theory of weighted Bergman space and obtain a general representation formula of the Bergman kernel function for the spaces on the Reinhardt domain containing the origin. As applications, we calculate the…

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…

The numerical performance of the material point method (MPM) is strongly governed by the particle-grid kernel, which controls the trade-off among smoothness, locality, numerical diffusion, contact accuracy, and computational cost. Although…

We present a technique for computing explicit, concrete formulas for the weighted Bergman kernel on a planar domain with weight the modulus squared of a meromorphic function in the case that the meromorphic function has a finite number of…

We prove that the norm of a weighted composition operator on the Hardy space H^2 of the disk is controlled by the norm of the weight function in the de Branges-Rovnyak space associated to the symbol of the composition operator. As a…

For a weight function in the unit disk which is the modulus of a finite product of powers of Blaschke factors, we give a canonical representation for the reproducing kernel of the corresponding weighted Bergman space in terms of the values…

These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…

Let $A$ be a $d \times d$ matrix with rational entries which has no eigenvalue $\lambda \in \mathbb{C}$ of absolute value $|\lambda| < 1$ and let $\mathbb{Z}^d[A]$ be the smallest nontrivial $A$-invariant $\mathbb{Z}$-module. We lay down a…

In this paper we obtain the closed forms of some hypergeometric functions. As an application, we obtain the explicit forms of the Bergman kernel functions for Reinhardt domains $\{|z_3|^{\lambda} < |z_1|^{2p} + |z_2|^2, \quad |z_1|^{2p} +…

We extend a classical result of Caughran/Schwartz and another recent result of Gunatillake by showing that if D is a bounded, convex domain in n-dimensional complex space, m is a holomorphic function on D and bounded away from zero toward…

The main aim of this article is to establish boundedness of singular integrals with non-smooth kernels on product spaces. Let $L_1$ and $L_2$ be non-negative self-adjoint operators on $L^2(\mathbb{R}^{n_1})$ and $L^2(\mathbb{R}^{n_2})$,…

We consider the problem of estimating the density $\Pi$ of a determinantal process $N$ from the observation of $n$ independent copies of it. We use an aggregation procedure based on robust testing to build our estimator. We establish…

Determinantal point processes (DPPs) are point process models that naturally encode diversity between the points of a given realization, through a positive definite kernel $K$. DPPs possess desirable properties, such as exact sampling or…

We view sequential design as a model selection problem to determine which new observation is expected to be the most informative, given the existing set of observations. For estimating a probability distribution on a bounded interval, we…

Adding a column of numbers produces "carries" along the way. We show that random digits produce a pattern of carries with a neat probabilistic description: the carries form a one-dependent determinantal point process. This makes it easy to…

We construct inner products by the Bernstein-Markov inequality on spaces of holomorphic sections of high powers of a line bundle. The corresponding weighted Bergman kernel functions converge to an extremal function. We obtain a uniform…