YANG LIU'S MATH BLOG

THE PROBABILISTIC ESTIMATES ON THE LARGEST AND SMALLEST q-SINGULAR VALUES OF RANDOM MATRICES

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In this paper, we study the q-singular values of random matrices with pre-Gaussian entries defined in terms of the q-quasinorm with 0 < q ≤ 1. In this paper, we mainly consider the decay of the lower and upper tail probabilities of the largest q-singular value s ^{(q)}_ 1 , when the number of rows of the matrices becomes very large. Based on the results in probabilistic estimates on the largest q-singular value, we also give probabilistic estimates on the smallest q-singular value for pre-Gaussian random matrices.

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