We derive analytic expressions for infinite products of random $2\times 2$ 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.

• Received 10 July 2002

DOI:https://doi.org/10.1103/PhysRevE.66.066124