Open Access
November, 1993 Products of 2×2 Random Matrices
David Mannion
Ann. Appl. Probab. 3(4): 1189-1218 (November, 1993). DOI: 10.1214/aoap/1177005279

Abstract

The notion of the shape of a triangle can be used to define the shape of a 2×2 real matrix; we find that the shape of a matrix retains just the right amount of information required for determining the main features of the asymptotic behaviour, as n, of GnGn1G1, where the Gi are i.i.d. copies of a 2×2 random matrix G. An alternative formula to the Furstenberg formula is proposed for the upper Lyapounov exponent of the probability distribution of G. We find that in some cases, using our formula, the Lyapounov exponent is more susceptible to explicit calculation.

Citation

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David Mannion. "Products of 2×2 Random Matrices." Ann. Appl. Probab. 3 (4) 1189 - 1218, November, 1993. https://doi.org/10.1214/aoap/1177005279

Information

Published: November, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0784.60019
MathSciNet: MR1241041
Digital Object Identifier: 10.1214/aoap/1177005279

Subjects:
Primary: 60D05
Secondary: 60J15

Keywords: Contracting subsets of , Lyapounov exponent , Products of random matrices , shape

Rights: Copyright © 1993 Institute of Mathematical Statistics

Vol.3 • No. 4 • November, 1993
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