Products of random matrices

We derive analytic expressions for infinite products of random 2 x 2 matrices. The determinant of the target matrix is log-normally distributed, whereas the remainder is a surprisingly complicated function of a parameter characterizing the norm of the matrix and a parameter characterizing its skewne...

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Published inPhysical review. E, Statistical, nonlinear, and soft matter physics Vol. 66; no. 6 Pt 2; p. 066124
Main Authors Jackson, A D, Lautrup, B, Johansen, P, Nielsen, M
Format Journal Article
LanguageEnglish
Published United States 01.12.2002
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Summary:We derive analytic expressions for infinite products of random 2 x 2 matrices. The determinant of the target matrix is log-normally distributed, whereas the remainder is a surprisingly complicated function of a parameter characterizing the norm of the matrix and a parameter characterizing its skewness. The distribution may have importance as an uncommitted prior in statistical image analysis.
ISSN:1539-3755
DOI:10.1103/PhysRevE.66.066124