02718nmm a2200325 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002100139245015900160250001700319260004200336300003200378505012600410653003800536653001500574653002300589653003200612653001600644700003300660041001900693989003800712490003700750028003000787856007200817082000800889520149500897EB000631044EBX0100000000000000048412600000000000000.0cr|||||||||||||||||||||140122 ||| eng a97814757238851 aHögnäs, Göran00aProbability Measures on Semigroups: Convolution Products, Random Walks and Random MatriceshElektronische Ressourcecby Göran Högnäs, Arunava Mukherjea a1st ed. 1995 aNew York, NYbSpringer USc1995, 1995 aXII, 388 pbonline resource0 a1. Semigroups -- 2. Probability Measures on Topological Semigroups -- 3. Random Walks on Semigroups -- 4. Random Matrices aTopological Groups and Lie Groups aLie groups aTopological groups aApplications of Mathematics aMathematics1 aMukherjea, Arunavae[author]07aeng2ISO 639-2 bSBAaSpringer Book Archives -20040 aUniversity Series in Mathematics50a10.1007/978-1-4757-2388-540uhttps://doi.org/10.1007/978-1-4757-2388-5?nosfx=yxVerlag3Volltext0 a519 aA 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. Miraculously, structured images appear briefly as we continue to apply the distortion procedure to successive images. After 241 iterations the original picture reappears, unchanged! Apparently the pixels of the Poincare portrait were moving about in accor dance with a strictly deterministic rule. More importantly, the set of all pixels, the whole portrait, was transformed by the distortion mechanism. In this exam ple the transformation seems to have been a reversible one since the original was faithfully recreated. It is not very farfetched to introduce a certain amount of randomness and irreversibility in the above example. Think of a random miscoloring of some pixels or of inadvertently giving a pixel the color of its neighbor. The methods in this book are geared towards being applicable to the asymp totics of such transformation processes. The transformations form a semigroup in a natural way; we want to investigate the long-term behavior of random elements of this semigroup