A generating function approach to the growth rate of random matrix products

Naranmandula Bao; Junbiao Lu; Yueheng Lan

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arXiv · 1911.00244

A generating function approach to the growth rate of random matrix products

Naranmandula Bao·Junbiao Lu·Yueheng Lan

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Abstract

Random matrix products arise in many science and engineering problems. An efficient evaluation of its growth rate is of great interest to researchers in diverse fields. In the current paper, we reformulate this problem with a generating function approach, based on which two analytic methods are proposed to compute the growth rate. The new formalism is demonstrated in a series of examples including an Ising model subject to on-site random magnetic fields, which seems very efficient and easy to implement. Through an extensive comparison with numerical computation, we see that the analytic results are valid in a regime of considerable size.

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Naranmandula Bao, Junbiao Lu, Yueheng Lan. 2019-11-01. A generating function approach to the growth rate of random matrix products. https://arxiv.org/abs/1911.00244

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