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Publications [#354026] of Hongkai Zhao

Papers Published

  1. 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)

    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 block-independent 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 block-independent 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 block-independent coordinates, and for random tensors.
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