Math @ Duke

Publications [#354026] of Hongkai Zhao
Papers Published
 Bryson, J; Vershynin, R; Zhao, H, Marchenko–Pastur law with relaxed independence conditions,
Random Matrices: Theory and Applications
(January, 2021), World Scientific Publishing [doi]
(last updated on 2021/08/03)
Abstract: We prove the Marchenko–Pastur law for the eigenvalues of p × p sample covariance matrices in two new situations where the data does not have independent coordinates. In the first scenario — the blockindependent model — the p coordinates of the data are partitioned into blocks in such a way that the entries in different blocks are independent, but the entries from the same block may be dependent. In the second scenario — the random tensor model — the data is the homogeneous random tensor of order d, i.e. the coordinates of the data are all (nd) different products of d variables chosen from a set of n independent random variables. We show that Marchenko–Pastur law holds for the blockindependent model as long as the size of the largest block is o(p), and for the random tensor model as long as d = o(n1/3). Our main technical tools are new concentration inequalities for quadratic forms in random variables with blockindependent coordinates, and for random tensors.


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