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

Publication date: Available online 10 October 2018Source: Statistics & Probability LettersAuthor(s): Ignacio ArbuésAbstractWe 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.

Source: Statistics and Probability Letters - October 11, 2018 Category: Statistics Source Type: research