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

Xingyuan Zeng

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 19, 4636-4647

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.

Date: 2020
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DOI: 10.1080/03610926.2019.1604962

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