Random point fields associated with certain Fredholm determinants I: fermion, Poisson and boson point processes

By Tomoyuki Shirai, Yoichiro Takahashi. 2003

365 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability

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Citations in the corpus

Determinantal Point Processes for Machine Learning (2012, background): “Many good mathematical surveys are now available [12, 68, 97, 132, 133, 137, 145].”
The Palm measure and the Voronoi tessellation for the Ginibre process (2006, neutral): “It follows from (8) (see [27]) that the Palm measure of a determinantal stationary process ψ with kernel K is the law of the process ψ 0 ∪ { 0 } where If P { ψ = ∅ is positive, then K (0 , 0) is positive.”
Determinantal probability measures (2002, methodology): “We also show that PQ has a trivial (full) tail σ-field for all Q; this was shown independently by Shirai and Takahashi (2003) when the spectrum of Q lies in (0, 1).”
On the topology of random complexes built over stationary point processes. (2012, neutral): “5) follows immediately from [37], Lemma 6.”
Determinantal Processes and Independence (2005, background): “Determinantal processes arise naturally in several other settings, including eigenvalues of random matrices, random spanning trees and nonintersecting paths; see, e.g., Burton and Pemantle [4], Soshnikov [27], Lyons [20], Lyons and Steif [21], Shirai and Takahashi [25], Johansson [14], Borodin, Okou”
Lectures on the Poisson Process (2017, background): “However, it is enough to assume that the associated integral operator is locally of trace class; see [150].”
Random point fields associated with certain Fredholm determinants II: Fermion shifts and their ergodic and Gibbs properties (2003, methodology): “13) one can easily compute the moments and correlation functions as is done in [17, 18].”
Zeros of Random Analytic Functions (2006, background): “21 process can be expressed as a mixture of determinantal processes with projection kernels (see (30),(31),(14)).”
Hyperdeterminantal point processes (2008, background): “minantalpointprocesseswereintroducedinMacchi(1975).Surveysoftheirproperties and numerous applications may be found in (Daley and Vere-Jones 1988; Soshnikov 2000; Lyons 2003; Hough et al. 2006; Shirai and Takahashi 2000, 2003a, b, 2004).”
The permanental process (2006, methodology): “The main difference between [27] and our paper is that the authors of the former began with a certain determinantal expansion due to Vere-Jones [32] and showed that it is the Laplace transform of a point process.”
Zeros of Gaussian Analytic Functions and Determinantal Point Processes (2009, background): “K is real, and defines a bounded, non-negative definite, symmetric, locally trace class integral operator K on Λ, and the measure μ on Λ is non-atomic, then 2 m determinantal processes also exist (75).”
Determinantal Point Processes (2016, background): “4 of [32], see also [7] for more details on the Fredholm determinant.”
On adding a list of numbers (and other one-dependent determinantal processes) (2009, background): “Lyons and Steif [52] and Shirai and Takahashi [65, 66] develop remarkable properties of the associated point process.”