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- W2951123721 abstract "We consider n-by-n matrices whose (i, j)-th entry is f(X_i^T X_j), where X_1, ...,X_n are i.i.d. standard Gaussian random vectors in R^p, and f is a real-valued function. The eigenvalue distribution of these random kernel matrices is studied at the large p, large n regime. It is shown that, when p and n go to infinity, p/n = gamma which is a constant, and f is properly scaled so that Var(f(X_i^T X_j)) is O(p^{-1}), the spectral density converges weakly to a limiting density on R. The limiting density is dictated by a cubic equation involving its Stieltjes transform. While for smooth kernel functions the limiting spectral density has been previously shown to be the Marcenko-Pastur distribution, our analysis is applicable to non-smooth kernel functions, resulting in a new family of limiting densities." @default.
- W2951123721 created "2019-06-27" @default.
- W2951123721 creator A5017106522 @default.
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- W2951123721 date "2012-02-14" @default.
- W2951123721 modified "2023-10-18" @default.
- W2951123721 title "The Spectrum of Random Inner-product Kernel Matrices" @default.
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- W2951123721 doi "https://doi.org/10.48550/arxiv.1202.3155" @default.
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