Functional central limit theorems and their associated large deviation principles for products of random matrices

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Abstract

This paper establishes a functional central limit theorem for a product of random matrices. The sequence of matrices form a stationary process which is a φ-mixing. The individual matrices in the product become closer and closer to the identity matrix with longer and longer products. In addition, these perturbations from the identity matrix have mean zero. A large deviation principle for the limit process is proved.

Original languageEnglish (US)
Pages (from-to)133-166
Number of pages34
JournalProbability Theory and Related Fields
Volume76
Issue number2
DOIs
StatePublished - Oct 1987
Externally publishedYes

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Products of Random Matrices
Functional Central Limit Theorem
Unit matrix
Large Deviation Principle
Stationary Process
Perturbation
Zero

ASJC Scopus subject areas

  • Statistics and Probability
  • Analysis
  • Mathematics(all)

Cite this

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abstract = "This paper establishes a functional central limit theorem for a product of random matrices. The sequence of matrices form a stationary process which is a φ-mixing. The individual matrices in the product become closer and closer to the identity matrix with longer and longer products. In addition, these perturbations from the identity matrix have mean zero. A large deviation principle for the limit process is proved.",
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