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Spectral distribution of large generalized random kernel matrices

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  • Zeng, Xingyuan

Abstract

We consider n×n random kernel matrix An whose entries are of form F(Xi,Xj)−unδij∑kF(Xi,Xk) with F(X,Y)=f(X′Y∕p) or f(|X−Y|2∕p) for i.i.d. random vectors Xi=Σp1∕2Yi∈Rp. Here f is a real-valued function, un is any real number which is allowed to change with n, Σp is a p×p positive semi-definite matrix and the entries of Yi’s are i.i.d. mean 0, variance 1 and have bounded m(m>4) absolute moments. Explicit limits of spectral distributions of generalized random kernel matrices are obtained in the case of p∕n→γ∈(0,∞) as p,n→∞.

Suggested Citation

  • Zeng, Xingyuan, 2019. "Spectral distribution of large generalized random kernel matrices," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 100-110.
    • Handle: RePEc:eee:stapro:v:152:y:2019:i:c:p:100-110
    DOI: 10.1016/j.spl.2019.04.016
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    References listed on IDEAS

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    1. Zeng, Xingyuan, 2014. "Distribution of eigenvalues of large Euclidean matrices generated from lp ellipsoid," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 181-191.
    2. Silverstein, J. W., 1995. "Strong Convergence of the Empirical Distribution of Eigenvalues of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 331-339, November.
    3. Zeng, Xingyuan, 2015. "A note on the large random inner-product kernel matrices," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 192-201.
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