Zeros of Gaussian Analytic Functions and Determinantal Point Processes

By John Hough, Manjunath Krishnapur, Yuval Peres, B'alint Vir'ag. University Lecture Series, 2009

640 citations recorded by the source corpus.

Subfields: Applied Mathematics, Discrete Mathematics and Combinatorics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8753b93eb3310f0f0a30474cbb019bf2ad81f551

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In Applied Mathematics

In Discrete Mathematics and Combinatorics

In Statistics and Probability

Citations in the corpus

Lectures on integrable probability (2012, background): “Nowadays lots of sources of determinantal point processes are known including (in addition to the random matrix theory) dimers on bipartite graphs [Kenyon-09], uniform spanning trees [Lyons-03], ensembles of non-intersecting paths on planar acyclic graphs [Johansson-02] and zeros of random analytic ”
Hyperuniform states of matter (2018, background): “, this “hole” probability is given by exp(−cr4) for large r [195].”
The Surprising Mathematics of Longest Increasing Subsequences (2015, neutral): “See [59], [80], [82], [81], [121] and [29, Section 5.”
On the topology of random complexes built over stationary point processes. (2012, methodology): “where the two equalities are due to [20] Theorem 4.”
On adding a list of numbers (and other one-dependent determinantal processes) (2009, neutral): “[43, 44] for details.”
Determinantal Point Processes (2016, methodology): “the seminal work of [17], along with the improvements found in [12], [18], [22].”
Spectral Radii of Large Non-Hermitian Random Matrices (2014, background): “Then A−1B is called a spherical ensemble [Hough et al. (2009)].”
Asymptotic distribution of complex zeros of random analytic functions (2014, background): “In this special case, the expected number of zeros of Fn in a Borel set B can be computed exactly [13, 33]:”
Determinantal processes and completeness of random exponentials: the critical case (2012, background): “For greater details on these point processes, see [HKPV10].”
Outliers in the spectrum of iid matrices with bounded rank perturbations (2010, methodology): “he constant coecient 1 by another complex gaussian g 0, then g(z) would be a Gaussian power series (GPS) in the variable 1=z. Gaussian power series have been intensively studied (see the recent text [29] and the references therein). In that case, the k-point correlation functions are given by the de”
Outlier Eigenvalues for Deformed I.I.D. Random Matrices (2014, methodology): “Following the terminology of Hough, Krishnapur, Peres, Virág [33], we say that g is a Gaussian analytic function on a domain Γ ⊂ C, if g is a random analytic function on Γ such that for every z1, · · · , zn in Γ, (g(z1), .”
Critical points of random polynomials with independent identically distributed roots (2012, background): “1 in [3]): for every analytic function f (which does not vanish identically),”