THE SPECTRUM OF RANDOM INNER-PRODUCT KERNEL MATRICES
Author(s): Cheng, Xiuyuan; Singer, Amit
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Full metadata record
DC Field | Value | Language |
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dc.contributor.author | Cheng, Xiuyuan | - |
dc.contributor.author | Singer, Amit | - |
dc.date.accessioned | 2019-08-29T17:01:20Z | - |
dc.date.available | 2019-08-29T17:01:20Z | - |
dc.date.issued | 2013-10 | en_US |
dc.identifier.citation | Cheng, Xiuyuan, Singer, Amit. (2013). THE SPECTRUM OF RANDOM INNER-PRODUCT KERNEL MATRICES. RANDOM MATRICES-THEORY AND APPLICATIONS, 2 (10.1142/S201032631350010X | en_US |
dc.identifier.issn | 2010-3263 | - |
dc.identifier.uri | http://arks.princeton.edu/ark:/88435/pr11143 | - |
dc.description.abstract | We consider nxn matrices whose (i, j)th entry is f(X-i(T) X-j), where X-1,..., X-n are i.i.d. standard Gaussian in R-p, and f is a real-valued function. The weak limit of the eigenvalue distribution of these random matrices is studied at the limit when p, n -> infinity and p/ n = gamma which is a constant. We show that, under certain conditions on the kernel function f, the limiting spectral density exists and is dictated by a cubic equation involving its Stieltjes transform. The parameters of this cubic equation are decided by a Hermite-like expansion of the rescaled kernel function. While the case that f is differentiable at the origin has been previously resolved by El Karoui [The spectrum of kernel random matrices, Ann. Statist. 38 (2010) 1-50], our result is applicable to non-smooth f, such as the Sign function and the hard thresholding operator of sample covariance matrices. For this larger class of kernel functions, we obtain a new family of limiting densities, which includes the Marcenko-Pastur (M.P.) distribution and Wigner’s semi-circle distribution as special cases. | en_US |
dc.language.iso | en_US | en_US |
dc.relation.ispartof | RANDOM MATRICES-THEORY AND APPLICATIONS | en_US |
dc.rights | Author's manuscript | en_US |
dc.title | THE SPECTRUM OF RANDOM INNER-PRODUCT KERNEL MATRICES | en_US |
dc.type | Journal Article | en_US |
dc.identifier.doi | doi:10.1142/S201032631350010X | - |
dc.date.eissued | 2013-12-06 | en_US |
dc.identifier.eissn | 2010-3271 | - |
pu.type.symplectic | http://www.symplectic.co.uk/publications/atom-terms/1.0/journal-article | en_US |
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