Zeros of Gaussian Analytic Functions and Determinantal Point Processes

No abstract is available for this paper.

• Publication year

  2009

• Venue

  University Lecture Series

• Publication date

  2009-10-13

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1090/ULECT/051
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Log-Gases and Random Matrices

  2010cited by this paper
• Asymptotics of the Hole Probability for Zeros of Random Entire Functions

  2009cited by this paper
• The Schur Algorithm in Terms of System Realizations

  2008cited by this paper
• Statistical properties of determinantal point processes in high-dimensional Euclidean spaces.

  2008cited by this paper
• The Jancovici–Lebowitz–Manificat Law for Large Fluctuations of Random Complex Zeroes

  2007influential reference
• Lectures on the Combinatorics of Free Probability

  2006cited by this paper
• Gravitational allocation to Poisson points

  2006cited by this paper
• Zeros of Random Analytic Functions

  2006cited by this paper
• Partition bijections, a survey

  2006cited by this paper
• Transportation to Random Zeroes by the Gradient Flow

  2005cited by this paper
• Random Matrices

  2005cited by this paper
• A Stable Marriage of Poisson and Lebesgue

  2005cited by this paper
• Determinantal Processes and Independence

  2005cited by this paper
• Overcrowding estimates for zeroes of Planar and Hyperbolic Gaussian analytic functions

  2005cited by this paper
• Large deviations for the zero set of an analytic function with diffusing coefficients

  2005cited by this paper
• Wiley Series in Probability and Mathematical Statistics

  2004cited by this paper
• Height Fluctuations in the Honeycomb Dimer Model

  2004cited by this paper
• PATTERNS IN EIGENVALUES: THE 70TH JOSIAH WILLARD GIBBS LECTURE

  2003cited by this paper
• Patterns in eigenvalues: the 70th Josiah Willard Gibbs lecture

  2003cited by this paper
• Random complex zeroes, III. Decay of the hole probability

  2003cited by this paper
• Random point fields associated with certain Fredholm determinants I: fermion, Poisson and boson point processes

  2003influential reference
• Zeros of the i.i.d. Gaussian power series: a conformally invariant determinantal process

  2003cited by this paper
• EQUILIBRIUM DISTRIBUTION OF ZEROS OF RANDOM POLYNOMIALS

  2002cited by this paper
• Local statistics of lattice dimers

  2001cited by this paper
• SPECIAL FUNCTIONS (Encyclopedia of Mathematics and its Applications 71)

  2001cited by this paper
• Uniform spanning forests

  2001cited by this paper
• A User's Guide to Measure Theoretic Probability by David Pollard

  2001cited by this paper
• Determinantal random point fields

  2000cited by this paper
• Non-intersecting paths, random tilings and random matrices

  2000cited by this paper
• Gaussian limit for determinantal random point fields

  2000cited by this paper
• Linear functionals of eigenvalues of random matrices

  2000cited by this paper
• Zeroes of Gaussian analytic functions

  2000cited by this paper
• Truncations of random unitary matrices

  1999cited by this paper
• GAUSSIAN HILBERT SPACES (Cambridge Tracts in Mathematics 129) By SVANTE JANSON: 340 pp., £40.00, ISBN 0 521 56128 0 (Cambridge University Press, 1997)

  1998cited by this paper
• Exact statistical properties of the zeros of complex random polynomials

  1998influential reference
• GAUSSIAN HILBERT SPACES (Cambridge Tracts in Mathematics 129) By SVANTE JANSON: 340 pp., £40.00, ISBN 0 521 56128 0 (Cambridge University Press, 1997)

  1998cited by this paper
• Two-Dimensional Coulomb Systems on a Surface of Constant Negative Curvature

  1998cited by this paper
• Gaussian Hilbert Spaces

  1997cited by this paper
• High powers of random elements of compact Lie groups

  1997cited by this paper
• Analytic Number Theory

  1997cited by this paper
• Chaotic analytic zero points: exact statistics for those of a random spin state

  1996cited by this paper
• Quantum chaotic dynamics and random polynomials

  1996cited by this paper
• Erratum to “How many zeros of a random polynomial are real?”

  1995cited by this paper
• Gaussian fluctuation in random matrices.

  1994cited by this paper
• On the Distribution of Roots of Random Polynomials

  1993cited by this paper
• Hyperbolic Geometry: FUCHSIAN GROUPS

  1993cited by this paper
• Complexity of Bezout’s Theorem II Volumes and Probabilities

  1993cited by this paper
• Probability: Theory and Examples

  1993cited by this paper
• Local Characteristics, Entropy and Limit Theorems for Spanning Trees and Domino Tilings Via Transfer-Impedances

  1993cited by this paper
• Complexity of Bézout’s theorem. I. Geometric aspects

  1993cited by this paper
• Large charge fluctuations in classical Coulomb systems

  1993cited by this paper
• Complexity of Bezout's Theorem: III. Condition Number and Packing

  1993cited by this paper
• Determinants and current flows in electric networks

  1992cited by this paper
• The two-dimensional Coulomb gas on a sphere: Exact results

  1992cited by this paper
• On the spectra of Gaussian matrices

  1992cited by this paper
• Probability with Martingales

  1991cited by this paper
• Resistances and currents in infinite electrical networks

  1990cited by this paper
• SOME RANDOM SERIES OF FUNCTIONS second edition (Cambridge Studies in Advanced Mathematics 5)

  1988influential reference
• Some Random Series of Functions

  1985cited by this paper
• Binomial Determinants, Paths, and Hook Length Formulae

  1985cited by this paper
• Complex analysis : an introduction to the theory of analytic functions of one complex variable / Lars V. Ahlfors

  1984cited by this paper
• Encyclopedia of Mathematics and its Applications.

  1982cited by this paper
• Exact results for a two-dimensional one-component plasma on a sphere

  1981cited by this paper
• Functional integration and quantum physics

  1979cited by this paper
• Norms of Gaussian sample functions

  1976cited by this paper
• States of classical statistical mechanical systems of infinitely many particles. II. Characterization of correlation measures

  1975cited by this paper
• The coincidence approach to stochastic point processes

  1975cited by this paper
• Correlation functions and the uniqueness of the state in classical statistical mechanics

  1973cited by this paper
• Quantum Physics

  1969cited by this paper
• Statistical Ensembles of Complex, Quaternion, and Real Matrices

  1965cited by this paper
• A and V

  1962cited by this paper
• Statistical Theory of the Energy Levels of Complex Systems. I

  1962cited by this paper
• The Threefold Way. Algebraic Structure of Symmetry Groups and Ensembles in Quantum Mechanics

  1962cited by this paper
• An Identity of Cayley

  1960cited by this paper
• Probability and Related Topics in Physical Sciences

  1960cited by this paper
• Fourier transforms in the complex domain

  1936cited by this paper
• Fourier Transforms in the Complex Domain

  1934cited by this paper
• Probability measures on metric spaces

  year unknowncited by this paper
• Bestimmung der symmetrischen Verbindungen vermittelst ihrer erzeugenden Function.

  year unknowncited by this paper
• Ueber die Auflösung der Gleichungen, auf welche man bei der Untersuchung der linearen Vertheilung galvanischer Ströme geführt wird

  year unknowncited by this paper

• Separation properties of a hybrid point process with determinantal radii and uniform arguments

  2026influential citation
• First passage times for decoupled random walks

  2026cites this paper
• Hole Phenomenon of Gaussian Analytic Functions with Power-exponential Weights

  2026cites this paper
• Holomorphic L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2$$\end{document} Signals of Several Complex Variables

  2026cites this paper
• Existence, properties, and parametric inference for possibly hyperuniform Gibbs perturbed lattices

  2026cites this paper
• Random points on $\mathbb{S}^3$ with small logarithmic energy

  2026cites this paper
• Improved well-posedness for the limit flow of differentiation of roots of polynomials

  2026cites this paper
• Zeros Of Random Analytic Functions And Spectral Properties Of Perturbed Unitary Matrices

  2025cites this paper
• Concentration of the number of real roots of random polynomials

  2025cites this paper
• How fast does spectral radius of truncated circular unitary ensemble converge?

  2025cites this paper
• The complex level crossings of random orthogonal polynomials

  2025cites this paper
• Bypassing orthogonalization in the quantum DPP sampler

  2025cites this paper
• Littlewood-type Theorems for Random Dirichlet Multipliers

  2025cites this paper
• NSB-H2GAN: “Negative Sample”-Boosted Hierarchical Heterogeneous Graph Attention Network for Interpretable Classification of Whole-Slide Images

  2025cites this paper
• On the spectral radius of the ratio of Girko matrices

  2025influential citation
• On the pair correlation statistics for determinantal point processes on the sphere

  2025cites this paper
• Limit theorems for decoupled renewal processes

  2025influential citation
• Separated determinantal point processes and generalized Fock spaces

  2025influential citation
• Edge limits of truncated circular beta ensembles

  2025cites this paper
• The Ginibre Ensemble Conditioned on an Overcrowding Event

  2025cites this paper
• Bayesian mixture models with repulsive and attractive atoms

  2025cites this paper
• Points on $\operatorname{SO}(3)$ with low logarithmic energy

  2025cites this paper
• Adaptive hyperparameter tuning for time-frequency algorithms based on the zeros of the spectrogram

  2025cites this paper
• Local repulsion between zeros and critical points of the Gaussian Entire Function

  2025influential citation
• On the distribution patterns of zeros for random polynomials with regularly varying coefficients

  2025influential citation
• Number variance for homogeneous determinantal processes on hyperbolic spaces

  2025influential citation
• Moderate deviations for weight-dependent random connection models

  2025cites this paper
• Sampling properties of the zeroes of the Gaussian entire function

  2025influential citation
• On Distances Among Slater Determinant States and Determinantal Point Processes

  2025cites this paper
• Universality of Outliers in Weakly Confined Coulomb-Type Systems

  2025cites this paper
• Weighted Point Configurations with Hyperuniformity: An Ecological Example and Models

  2025cites this paper
• The asphericity of locally finite infinite configuration spaces and Weierstrass entire coverings

  2025cites this paper
• Indistinguishability of unbounded components in the occupied and vacant sets of Boolean models on symmetric spaces

  2025influential citation
• Partial Bergman kernels and determinantal point processes on K\"ahler manifolds

  2025influential citation
• A simple proof of local universality for roots of Kac polynomials

  2025cites this paper
• Spectral representation of correlation functions for zeros of Gaussian power series with stationary coefficients

  2025influential citation
• The density of zeros of random power series with stationary complex Gaussian coefficients

  2025cites this paper
• Uniform convergence of Dyson Ferrari–Spohn diffusions to the Airy line ensemble

  2025cites this paper
• Filtering through a topological lens: homology for point processes on the time-frequency plane

  2025cites this paper
• Maximum gap in complex Ginibre matrices

  2025influential citation
• Electrostatic computations for statistical mechanics and random matrix applications

  2025influential citation
• Optimal transport, determinantal point processes and the Bergman kernel

  2025cites this paper
• Optimal matchings of randomly perturbed lattices

  2025influential citation
• On local large deviations for decoupled random walks

  2025influential citation
• Explicit description of Christoffel deformations and Palm measures of the Plancherel measure, the z–measures and the Gamma process

  2025cites this paper
• The Analytic Stockwell Transform and its zeros

  2024influential citation
• On the logarithmic energy of solutions to the polynomial eigenvalue problem

  2024influential citation
• Universal statistics of hippocampal place fields across species and dimensionalities

  2024cites this paper
• Multiple Sampling and Interpolation in a Space of Polynomials

  2024cites this paper
• Ensemble inter-relations in random matrix theory

  2024influential citation
• On determinantal point processes with nonsymmetric kernels

  2024influential citation
• On accumulated spectrograms for Gabor frames

  2024cites this paper
• Bayesian strategies for repulsive spatial point processes

  2024cites this paper
• The directed landscape is a black noise

  2024influential citation
• Rigidity of random stationary measures and applications to point processes

  2024influential citation
• Hyperuniform point sets on projective spaces

  2024cites this paper
• Monte Carlo methods on compact complex manifolds using Bergman kernels

  2024cites this paper
• Equidistribution of points in the Harmonic ensemble for the Wasserstein distance

  2024influential citation
• Layer-diverse Negative Sampling for Graph Neural Networks

  2024cites this paper
• Riesz energy, L2$L^2$ discrepancy, and optimal transport of determinantal point processes on the sphere and the flat torus

  2024cites this paper
• Eigenvalues of product of Ginibre ensembles and their inverses and that of truncated Haar unitary matrices and their inverses

  2024cites this paper
• Number rigid determinantal point processes induced by generalized Cantor sets

  2024cites this paper
• A Greedy Approximation for k-Determinantal Point Processes

  2024cites this paper
• Point Processes and spatial statistics in time-frequency analysis

  2024influential citation
• Large charge fluctuations in the hierarchical Coulomb gas

  2024cites this paper
• A strong law of large numbers for real roots of random polynomials

  2024cites this paper
• Torsion-weighted spanning acycle entropy in cubical lattices and Mahler measures

  2024cites this paper
• Large prime factors of well-distributed sequences

  2024cites this paper
• Hole event for random holomorphic sections on compact Riemann surfaces

  2024cites this paper
• Concentration of the number of real roots of random polynomials

  2024cites this paper
• On Decoupled Standard Random Walks

  2024influential citation
• Couplings and Poisson approximation for stabilising functionals of determinantal point processes

  2024cites this paper
• Hyperuniformity and optimal transport of point processes

  2024influential citation
• Benchmarking multi-component signal processing methods in the time-frequency plane

  2024cites this paper
• Repulsion, chaos, and equilibrium in mixture models

  2024cites this paper
• Computation of marginal eigenvalue distributions in the Laguerre and Jacobi $\beta$ ensembles

  2024influential citation
• On the Wasserstein distance between a hyperuniform point process and its mean

  2024cites this paper
• Arithmetic Consequences of the GUE Conjecture for Zeta Zeros

  2024cites this paper
• A Law of large numbers for vector-valued linear statistics of Bergman DPP

  2024influential citation
• Zeros of random polynomials undergoing the heat flow

  2023cites this paper
• Mean and variance of the cardinality of particles in infinite true polyanalytic Ginibre processes via a coherent states quantization method

  2023cites this paper
• Repelled point processes with application to numerical integration

  2023influential citation
• Rédacteurs en chef / Chief Editors

  2023cites this paper
• A determinantal point process approach to scaling and local limits of random Young tableaux

  2023cites this paper
• Concentration for the zero set of large random polynomial systems

  2023cites this paper
• Entanglement entropy and hyperuniformity of Ginibre and Weyl–Heisenberg ensembles

  2023cites this paper
• Laws of the iterated and single logarithm for sums of independent indicators, with applications to the Ginibre point process and Karlin’s occupancy scheme

  2023influential citation
• Hole radii for the Kac polynomials and derivatives

  2023cites this paper
• Liquid-gas phase transition for Gibbs point process with Quermass interaction

  2023cites this paper
• GAUSSIAN HOLOMORPHIC SECTIONS ON NONCOMPACT COMPLEX MANIFOLDS

  2023cites this paper
• QMC strength for some random configurations on the sphere

  2023cites this paper
• Scaling limits of stationary determinantal shot-noise fields

  2023cites this paper
• Determinantally equivalent nonzero functions

  2023cites this paper
• On p-frame potentials of the Beltrán and Etayo point processes on the sphere

  2023cites this paper
• Stochastic analysis of infinite particle systems—A new development in classical stochastic analysis and dynamical universality of random matrices

  2023cites this paper
• Real roots of random polynomials: Asymptotics of the variance

  2023influential citation
• Inradius of random lemniscates

  2023cites this paper
• Fluctuations in the logarithmic energy for zeros of random polynomials on the sphere

  2023influential citation
• Minorization-Maximization for Learning Determinantal Point Processes

  2023cites this paper
• On convergence of points to limiting processes, with an application to zeta zeros

  2023cites this paper