ON THE DENSITY OF EIGENVALUES OF A RANDOM MATRIX

By M. L. Mehta, M. Gaudin. 1960

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Citations in the corpus

Determinantal Point Processes for Machine Learning (2012, background): “Eigenvalues of random matrices [Ginibre, 1965, Mehta and Gaudin, 1960] Let M be a random matrix obtained by drawing every entry independently from the complex normal distribution.”
A Dynamical Approach to Random Matrix Theory (2017, methodology): “Behind the spectacular progress in understanding the local statistics of invariant ensembles, the cornerstone of this approach lies in the fact that there are explicit formulas to represent eigenvalue correlation functions by orthogonal polynomials – a key observation made in the original work of Ga”
Polynomial convolutions and (nite) free probability (2021, background): “Secondly, we remark that it should come as no surprise that the corresponding polynomial should be the Hermite polynomial, since the root distribution must converge asymptotically to the semicircle law (the free probability version of the Gaussian), and it is well known that the roots of the Hermite”
Eigenvalue statistics for beta-ensembles (2003, unknown): “Aside from the limiting level density, finite n exact level densities for each one of the three ensembles are known, due to Gaudin [33] and Mehta [67]; asymptotics for the level densities have also been explored by Basor, Tracy, and Widom [9].”
The local relaxation flow approach to universality of the local statistics for random matrices (2009, methodology): “This approach was originally applied to classical ensembles by Dyson [13], Mehta and Gaudin [31] and Mehta [30] that lead to classical orthogonal polynomials.”
Fixed Energy Universality for Generalized Wigner Matrices (2014, background): “In the fundamental particular case where HN is a real symmetric matrix from the Gaussian Orthogonal Ensemble (GOE), the correlation functions are known to converge on microscopic scales, the limit being expressible as a determinant [6, 7, 27, 28]: for any v ∈ R and E ∈ (−2, 2), we have”
The Steepest Descent Method for Orthogonal Polynomials on the Real Line with Varying Weights (2008, background): “[17] M. L. Mehta and M. Gaudin, “On the density of eigenvalues of a random matrix,” Nuclear Phys., 18, 420–427, 1960.”
Fast Greedy MAP Inference for Determinantal Point Process to Improve Recommendation Diversity (2017, methodology): “Besides its early applications in quantum physics and random matrices [35], it has also been recently applied to various machine learning tasks such as multiple-person pose estimation [27], image search [28], document summarization [29], video summarization [19], product recommendation [18], and twe”
Random matrices: Universality of local eigenvalue statistics (2009, background): “Indeed, it was established by Gaudin and Mehta [34] that (10) ρ n (x1, .”
Bulk universality for generalized Wigner matrices (2010, unknown): “[3, 6, 7, 8, 9, 25, 26, 27] and references therein).”
Universality of Wigner random matrices: a survey of recent results (2010, methodology): “This approach was originally applied by Mehta and Gaudin [70, 72] to compute the gap distribution for the Gaussian case that involved classical Hermite orthonormal polynomials.”
Universality of local spectral statistics of random matrices (2011, methodology): “In particular, the WignerDyson-Gaudin-Mehta (WDGM) conjecture for Hermitian matrices was first solved in [27] in a joint work with the current authors and Péché, Ramı́rez, and Schlein.”