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arXiv · 2104.02707

Macroscale behavior of random lower triangular matrices

J. E. Pascoe·Tapesh Yadav
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Abstract

We analyze the macroscale behavior of random lower (and therefore upper) triangular matrices with entries drawn iid from a distribution with nonzero mean and finite variance. We show that such a matrix behaves like a probabilistic version of a Riemann sum and therefore in the limit behaves like the Volterra operator. Specifically, we analyze certain SOT-like and WOT-like modes of convergence for random lower triangular matrices to a scaled Volterra operator. We close with a brief discussion of moments.

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J. E. Pascoe, Tapesh Yadav. 2021-04-06. Macroscale behavior of random lower triangular matrices. https://arxiv.org/abs/2104.02707

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