Probability Measures on Semigroups: Convolution Products, Random Walks and Random Matrices

A Scientific American article on chaos, see Crutchfield et al. (1986), illus­ trates a very persuasive example of recurrence. A painting of Henri Poincare, or rather a digitized version of it, is stretched and cut to produce a mildly distorted image of Poincare. The same procedure is applied to the distorted image and the process is repeated over and over again on the successively more and more blurred images. After a dozen repetitions nothing seems to be left of the original portrait. Miraculou