Results 321 to 330 of about 8,436,612 (364)

Nonlinear random matrix theory for deep learning

Neural Information Processing Systems, 2019
Neural network configurations with random weights play an important role in the analysis of deep learning. They define the initial loss landscape and are closely related to kernel and random feature methods. Despite the fact that these networks are built
Jeffrey Pennington, Pratik Worah
semanticscholar   +1 more source

“Random” random matrix products

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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Random matrix theory

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.
Alan Edelman, N. Raj Rao
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Generating Matrix Exponential Random Variates

SIMULATION, 1998
In this paper we present a technique for generating random variates from an empirical distribution using the matrix exponential representation of the distribution. In our experience, a matrix exponential representation of an empirical distribution produces random variates with an excellent fit with the empirical distribution.
Brown, E., Place, J., Van de Liefvoort, A.   +2 more
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Matrix Randomization Methods

2013
This chapter presents algorithms for uniform matrix sample generation in norm-bounded sets. First, we discuss the simple case of matrix sampling in sets defined by l p Hilbert–Schmidt norm, which reduces to the vector l p norm randomization problem. Subsequently, we present an efficient solution to the problem of uniform generation in sets defined by ...
Roberto Tempo, Giuseppe Calafiore, Fabrizio Dabbene   +2 more
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Matrix realization of random surfaces

Physical Review D, 1991
The large-N one-matrix model with a potential V(φ)=φ 2 /2+g 4 φ 4 /N+g 6 φ 6 /N 2 is carefully investigated using the orthogonal polynomial method. We present a numerical method to solve the recurrence relation and evaluate the recursion coefficients r k (k=1,2,3,...) of the orthogonal polynomials at large N.
, Sasaki, , Suzuki
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Random Matrix Theory

1992
Before about 1956, there was no systematic statistical theory of nuclear energy level structure. There was a shortage of close spacings in experimentally obtained energy levels which was generally dismissed as being due to instrumental resolution failings.
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Random Matrix Thermodynamics

AIP Conference Proceedings, 2006
We have performed a study of the statistical mechanics of correlated spectra first introduced by Dyson and Mehta some 40 years ago. We have derived a modified thermodynamical statistics (a number and its variance) for linear spectra. This approach was used to analyze the statistical properties of the eigenvalues of random matrices of Gaussian ensembles
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Random-Matrix Theory

2001
A wealth of empirical and numerical evidence suggests universality for local fluctuations in quantum energy or quasi-energy spectra of systems that display global chaos in their classical phase spaces. Exceptions apart, all such Hamiltonian matrices of sufficiently large dimension yield the same spectral fluctuations provided they have the same group ...
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Random Matrix Theory and Wireless Communications

Foundations and Trends in Communications and Information Theory, 2004
A. Tulino, S. Verdú
semanticscholar   +1 more source