58,402 research outputs found
Convergence of the empirical spectral distribution function of Beta matrices
Let ,
where and are two independent sample covariance
matrices with dimension and sample sizes and , respectively. This is
the so-called Beta matrix. In this paper, we focus on the limiting spectral
distribution function and the central limit theorem of linear spectral
statistics of . Especially, we do not require or
to be invertible. Namely, we can deal with the case where
and . Therefore, our results cover many important
applications which cannot be simply deduced from the corresponding results for
multivariate matrices.Comment: Published at http://dx.doi.org/10.3150/14-BEJ613 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
An Infinite Dimensional Approach to the Third Fundamental Theorem of Lie
We revisit the third fundamental theorem of Lie (Lie III) for finite
dimensional Lie algebras in the context of infinite dimensional matrices.Comment: This is a contribution to the Proc. of the Seventh International
Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007,
Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
Dwork crystals I
We present an elementary elaboration of Dwork's idea of explicit -adic
limit formulas for zeta functions of toric hypersurfaces.Comment: This version is identical with the earlier one, we only change the
numeration of theorems so that it agrees with the version published by IMR
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