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

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  • Arbués, Ignacio

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.

Suggested Citation

  • Arbués, Ignacio, 2019. "Central limit theorem for the entries of products of random matrices without the positivity condition," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 254-259.
    • Handle: RePEc:eee:stapro:v:145:y:2019:i:c:p:254-259
    DOI: 10.1016/j.spl.2018.09.014
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