Gaussian limit for determinantal random point fields

By Alexander Soshnikov. 2000

174 citations recorded by the source corpus.

Author(s): Soshnikov, Alexander | Abstract: We prove that under fairly general conditions properly rescaled determinantal random point field converges to a generalized Gaussian random process.

Subfields: Geometry and Topology, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/bba50c0965b2a3d9ad5d13534e0c61b34df191a1

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In Geometry and Topology

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Random point fields associated with certain Fredholm determinants II: Fermion shifts and their ergodic and Gibbs properties (2003, background): “The following two propositions are discrete versions of the propositions proved in our previous paper [18] and found in a somewhat more general setting in [23].”
Gaussian fluctuations for non-Hermitian random matrix ensembles (2005, unknown): “We cite [3, 7, 16, 20, 23, 27 ]a nd [ 28 ] as a representative list.”
Zeros of Gaussian Analytic Functions and Determinantal Point Processes (2009, methodology): “1 ((15), (84)) used the moment generating function for particle counts.”
Random matrices: Universality of local spectral statistics of non-Hermitian matrices (2012, background): “From the general Costin-Lebowitz central limit theorem for determinantal point processes [12], [47], [48] we know that NB(z0,r) −ENB(z0,r) (VarNB(z0,r)) 1/2 → N(0, 1)R provided that VarNB(z0,r) → ∞; indeed, an inspection of the proof in [48] gives the slightly stronger assertion that”
Monte Carlo with determinantal point processes (2016, background): “See for instance [Johansson, 1997, 1998, Diaconis and Evans, 2001, Soshnikov, 2002, Pastur, 2006, Rider and Virág, 2007, Popescu, 2009, Kriecherbauer and Shcherbina, 2010, Ameur et al., 2011, 2015, Berman, 2012, Shcherbina, 2013, Breuer and Duits, 2013, 2014, Johansson and Lambert, 2015, Lambert,…”
Fluctuations of eigenvalues and second order Poincaré inequalities (2007, background): “(Sinăı and Soshnikov [47], Theorem 2) Let Xij and An be as above.”
Determinantal Processes and Independence (2005, methodology): “Existing proofs of results of the kind of Theorem 24 ([5], [28]) use the moment generating function for particle counts.”
Gaussian Limits for Random Measures in Geometric Probability (2005, unknown): “Lemma 3 of [28]).”