Results 321 to 330 of about 8,171,715 (369)
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100 Years of Math Milestones, 2016
In this chapter the Gaussian random matrix ensembles are investigated. We determine their Green’s functions and show that for small energy differences a soft mode appears. As a consequence, the non-linear sigma-model is introduced and the level correlations are determined.
Franz Wegner
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In this chapter the Gaussian random matrix ensembles are investigated. We determine their Green’s functions and show that for small energy differences a soft mode appears. As a consequence, the non-linear sigma-model is introduced and the level correlations are determined.
Franz Wegner
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VeRA: Vector-based Random Matrix Adaptation
International Conference on Learning Representations, 2023Low-rank adapation (LoRA) is a popular method that reduces the number of trainable parameters when finetuning large language models, but still faces acute storage challenges when scaling to even larger models or deploying numerous per-user or per-task ...
Dawid J. Kopiczko +2 more
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Tracking of Extended Object Using Random Matrix With Non-Uniformly Distributed Measurements
IEEE Transactions on Signal Processing, 2021Extended object tracking (EOT) is gaining momentum in recent years. The random matrix method is a popular EOT method, which has a simple yet effective framework.
Le Zhang, Jian Lan
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On the Distribution of a Random Matrix
Communications in Statistics - Simulation and Computation, 1975Let Y1 and Y2 be distributed as independent normal p-vectors with the means respectively and with the same covariance matrix Σ and let S be distributed as Wishart Wp (N1+N2 −2,Σ), independent of Y1 and Y2. In this paper an analytic derivation of the distribution of the 2×2 matrix M=Y'S−1 γ where Y = (Y1, Y2) and μ and ν are arbitrary vectors is given ...
Narayan C. Giri, Bimal K. Sinha
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A First Course in Random Matrix Theory
, 2020The real world is perceived and broken down as data, models and algorithms in the eyes of physicists and engineers. Data is noisy by nature and classical statistical tools have so far been successful in dealing with relatively smaller levels of ...
M. Potters, J. Bouchaud
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“Random” random matrix products [PDF]
Journal d'Analyse Mathématique, 2001 This paper studies compositions of independent random bundle maps \(F(x,a)=f_Fx,T_F(x)a\), \(x\in X\), \(a\in \mathbb R^d\), where \(X\) is a Borel subset of a Polish space, whose distributions form a stationary process. This specializes to the case of products of independent random matrices evolving by a stationary process and generalizes many results
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Extended Object Tracking Using Random Matrix With Skewness
IEEE Transactions on Signal Processing, 2020For extended object tracking, the random matrix approach is a computationally efficient framework that is capable of estimating the kinematic state, and extension of the object jointly, and thus is gaining momentum in recent years. Existing random matrix
Le Zhang, Jian Lan
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ON THE DENSITY OF EIGENVALUES OF A RANDOM MATRIX
Nuclear Physics, 1960Abstract An exact expression for the density of eigenvalues of a random-matrix is derived. When the order of the matrix becomes infinite, it can be seen very directly that it goes over to Wigner's “semi-circle law”.
Michel Gaudin, Madan Lal Mehta
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2017
Random matrix theory deals with the study of matrix-valued random variables. It is conventionally considered that random matrix theory dates back to the work of Wishart in 1928 [1] on the properties of matrices of the type XX † with X ε ℂ N×n a random matrix with independent Gaussian entries with zero mean and equal variance.
Couillet, Romain, Debbah, Merouane
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Random matrix theory deals with the study of matrix-valued random variables. It is conventionally considered that random matrix theory dates back to the work of Wishart in 1928 [1] on the properties of matrices of the type XX † with X ε ℂ N×n a random matrix with independent Gaussian entries with zero mean and equal variance.
Couillet, Romain, Debbah, Merouane
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Acta Numerica, 2005 Random matrix theory is now a big subject with applications in many disciplines of science, engineering and finance. This article is a survey specifically oriented towards the needs and interests of a numerical analyst. This survey includes some original material not found anywhere else.
N. Raj Rao, Alan Edelman
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