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A note on the large random inner-product kernel matrices

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  • Zeng, Xingyuan

Abstract

In this note we consider the n×n random matrices whose (i,j)th entry is f(xiTxj), where xi’s are i.i.d. random vectors in RN, and f is a real-valued function. The empirical spectral distributions of these random inner-product kernel matrices are studied in two kinds of high-dimensional regimes: n/N→γ∈(0,∞) and n/N→0 as both n and N go to infinity. We obtain the limiting spectral distributions for those matrices from different random vectors in RN including the points lp-norm uniformly distributed over four manifolds. And we also show a result on isotropic and log-concave distributed random vectors, which confirms a conjecture by Do and Vu.

Suggested Citation

  • Zeng, Xingyuan, 2015. "A note on the large random inner-product kernel matrices," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 192-201.
    • Handle: RePEc:eee:stapro:v:99:y:2015:i:c:p:192-201
    DOI: 10.1016/j.spl.2015.01.014
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    References listed on IDEAS

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    1. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
    2. Zeng, Xingyuan, 2014. "Distribution of eigenvalues of large Euclidean matrices generated from lp ellipsoid," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 181-191.
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    Cited by:

    1. Zeng, Xingyuan, 2019. "Spectral distribution of large generalized random kernel matrices," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 100-110.

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