Large deviations upper bounds and central limit theorems for non-commutative functionals of Gaussian large random matrices

By Alice Guionnet. 2002

90 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8fcba8c8ea0e2d97162ad6dcb2ad93d43c7f290d

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In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Singularities of Solutions to Quadratic Vector Equations on the Complex Upper Half‐Plane (2015, background): “1) see [24, 37] (in the Gaussian setting), [7] (with the additional condition that the fourth moments have a profile), and [5] (with bounded higher moments).”
Second order asymptotics for matrix models (2006, background): “Note that a similar formula for the variance of the central limit theorem governing the fluctuations of words of band matrices was found in [13].”
Regularity conditions in the CLT for linear eigenvalue statistics of Wigner matrices (2012, background): “In recent years, several authors have derived central limit theorems for centred linear eigenvalue statistics of Wigner matrices with various hypotheses, see [1], [5], [7], [6], [9], [20], [21], [26], [29], [31], [32].”
GLOBAL FLUCTUATIONS FOR LINEAR STATISTICS OF β-JACOBI ENSEMBLES (2012, methodology): “MR2641363 (2011d:82001) [21] Alice Guionnet, Large deviations upper bounds and central limit theorems for non-commutative functionals of Gaussian large random matrices, Ann.”
Fluctuations of eigenvalues and second order Poincaré inequalities (2007, methodology): “The ideas were used by Guionnet [26] to prove central limit theorems for certain band matrix models.”
Central Limit Theorems for Linear Statistics of Heavy Tailed Random Matrices (2013, background): “Finally, but this is not really our concern here, the fluctuations of the trace of words in several random matrices were studied in [18, 28, 38, 29].”
CENTRAL LIMIT THEOREM FOR LINEAR EIGENVALUE STATISTICS OF RANDOM MATRICES WITH INDEPENDENT ENTRIES (2008, background): “In the last decade a number of results on the CLT for linear eigenvalue statistics of various classes of random matrices has been obtained (see [2, 5, 7, 8, 10, 11, 13, 15, 16, 17, 18, 28, 29, 30] and [31] and the references therein).”