Spectral distribution of large generalized random kernel matrices

Xingyuan Zeng

Statistics & Probability Letters, 2019, vol. 152, issue C, 100-110

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→∞.

Keywords: Random matrices; Empirical spectral distribution; Laplacian; Kernel matrices; High dimension regime (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spl.2019.04.016

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