Displaying similar documents to “Matrix kernels for the Gaussian orthogonal and symplectic ensembles”

Central limit theorems for eigenvalues in a spiked population model

Zhidong Bai, Jian-Feng Yao (2008)

Annales de l'I.H.P. Probabilités et statistiques

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In a spiked population model, the population covariance matrix has all its eigenvalues equal to units except for a few fixed eigenvalues (spikes). This model is proposed by Johnstone to cope with empirical findings on various data sets. The question is to quantify the effect of the perturbation caused by the spike eigenvalues. A recent work by Baik and Silverstein establishes the almost sure limits of the extreme sample eigenvalues associated to the spike eigenvalues when the population...

Harmonic analysis in value at risk calculations.

Claudio Albanese, Luis Seco (2001)

Revista Matemática Iberoamericana

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Value at Risk is a measure of risk exposure of a portfolio and is defined as the maximum possible loss in a certain time frame, typically 1-20 days, and within a certain confidence, typically 95%. Full valuation of a portfolio under a large number of scenarios is a lengthy process. To speed it up, one can make use of the total delta vector and the total gamma matrix of a portfolio and compute a Gaussian integral over a region bounded by a quadric. We use methods from harmonic analysis...

The solution of the Kato problem in two dimensions.

Steve Hofmann, Alan McIntosh (2002)

Publicacions Matemàtiques

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We solve, in two dimensions, the "square root problem of Kato". That is, for L ≡ -div (A(x)∇), where A(x) is a 2 x 2 accretive matrix of bounded measurable complex coefficients, we prove that L1/2: L1 2(R2) → L2(R2). [Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial...