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Spectrum of large random inner-product kernel matrices generated from lp ellipsoids

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  • Xingyuan Zeng

Abstract

In this note, we study the n × n random kernel matrix whose (i,j)th entry is of form f(xi′xj)−unδij∑kf(xi′xk) for some real function f and the xi’s are i.i.d. random vectors generated from lp ellipsoid or its surface in RN. The limit of the empirical spectral distribution is derived in the regime where n and N grow proportionally to infinity. Here un is allowed to be any real number which includes the two most interesting cases un = 0 and un = 1. Besides, compared with the existing related work, our results require only minimal regularity assumptions on the kernel function f.

Suggested Citation

  • Xingyuan Zeng, 2020. "Spectrum of large random inner-product kernel matrices generated from lp ellipsoids," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(19), pages 4636-4647, October.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:19:p:4636-4647
    DOI: 10.1080/03610926.2019.1604962
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