Central limit theorem for the entries of products of random matrices without the positivity condition

Ignacio Arbués

Statistics & Probability Letters, 2019, vol. 145, issue C, 254-259

Abstract: We prove a Central Limit Theorem for the entries of products of i.i.d. random matrices, in which the factors may have both positive and negative elements. We focus in the case that the distribution of the matrices has a density. The theorem is proved by representing the products as Markov Chains and establishing a variational inequality for a certain Lyapunov function.

Keywords: Random matrix; Central limit theorem; Markov chain (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spl.2018.09.014

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