# Partial isometries, duality, and determinantal point processes

@article{Katori2021PartialID, title={Partial isometries, duality, and determinantal point processes}, author={Makoto Katori and Tomoyuki Shirai}, journal={Random Matrices: Theory and Applications}, year={2021} }

A determinantal point process (DPP) is an ensemble of random nonnegative-integer-valued Radon measures [Formula: see text] on a space [Formula: see text] with measure [Formula: see text], whose correlation functions are all given by determinants specified by an integral kernel [Formula: see text] called the correlation kernel. We consider a pair of Hilbert spaces, [Formula: see text], which are assumed to be realized as [Formula: see text]-spaces, [Formula: see text], [Formula: see text], and…

## 8 Citations

### Determinantal Point Processes, Stochastic Log-Gases, and Beyond

- Mathematics
- 2020

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…

### Hyperuniformity of the determinantal point processes associated with the Heisenberg group

- Mathematics
- 2022

The Ginibre point process is given by the eigenvalue distribution of a nonhermitian complex Gaussian matrix in the infinite matrix-size limit. This is a determinantal point process (DPP) on the…

### New boundaries for positive definite functions

- Mathematics, Computer Science
- 2019

The authors' results entail an analysis of a partial order on families of p.d. kernels, a duality for operators and frames, optimization, Karhunen--Lo--Lo expansions, and factorizations, and an identification of optimal feature spaces in machine learning models.

### Harmonic analysis of network systems via kernels and their boundary realizations

- Computer ScienceDiscrete and Continuous Dynamical Systems - Series S
- 2021

New tools for realizations and transforms of positive definite kernels (p.d.) of infinite network/graph models, a duality for operators and frames, optimization, Karhunen–Loève expansions, and factorizations are introduced.

### Local number variances and hyperuniformity of the Heisenberg family of determinantal point processes

- Mathematics
- 2021

The bulk scaling limit of eigenvalue distribution on the complex plane C of the complex Ginibre random matrices provides a determinantal point process (DPP). This point process is a typical example…

### Circulant L-ensembles in the thermodynamic limit

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2021

L-ensembles are a class of determinantal point processes which can be viewed as a statistical mechanical systems in the grand canonical ensemble. Circulant L-ensembles are the subclass which are…

### Zeros of the i.i.d. Gaussian Laurent Series on an Annulus: Weighted Szegő Kernels and Permanental-Determinantal Point Processes

- ArtCommunications in Mathematical Physics
- 2022

On an annulus Aq:={z∈C:q<|z|<1}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}…

### Local Maxima of White Noise Spectrograms and Gaussian Entire Functions

- MathematicsJournal of Fourier Analysis and Applications
- 2022

We confirm Flandrin’s prediction for the expected average of local maxima of spectrograms of complex white noise with Gaussian windows (Gaussian spectrograms or, equivalently, modulus of weighted…

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