Probability Measures on Semigroups: Convolution Products, Random Walks, and Random Matrices
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Springer US
1995
|
| Schriftenreihe: | The University Series in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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. 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 |
| Beschreibung: | 1 Online-Ressource (XII, 388 p) |
| ISBN: | 9781475723885 9781475723908 |
| DOI: | 10.1007/978-1-4757-2388-5 |
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Datensatz im Suchindex
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|---|---|
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| author | Högnäs, Göran |
| author_facet | Högnäs, Göran |
| author_role | aut |
| author_sort | Högnäs, Göran |
| author_variant | g h gh |
| building | Verbundindex |
| bvnumber | BV042421336 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1184482617 (DE-599)BVBBV042421336 |
| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4757-2388-5 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781475723885 9781475723908 |
| language | English |
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| spelling | Högnäs, Göran Verfasser aut Probability Measures on Semigroups Convolution Products, Random Walks, and Random Matrices by Göran Högnäs, Arunava Mukherjea Boston, MA Springer US 1995 1 Online-Ressource (XII, 388 p) txt rdacontent c rdamedia cr rdacarrier The University Series in Mathematics 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. 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 Statistics Mathematics Statistics, general Mathematics, general Mathematik Statistik Halbgruppe (DE-588)4022990-7 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd rswk-swf Halbgruppe (DE-588)4022990-7 s Wahrscheinlichkeitsmaß (DE-588)4137556-7 s 1\p DE-604 Wahrscheinlichkeitstheorie (DE-588)4079013-7 s 2\p DE-604 Mukherjea, Arunava Sonstige oth https://doi.org/10.1007/978-1-4757-2388-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Högnäs, Göran Probability Measures on Semigroups Convolution Products, Random Walks, and Random Matrices Statistics Mathematics Statistics, general Mathematics, general Mathematik Statistik Halbgruppe (DE-588)4022990-7 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd |
| subject_GND | (DE-588)4022990-7 (DE-588)4079013-7 (DE-588)4137556-7 |
| title | Probability Measures on Semigroups Convolution Products, Random Walks, and Random Matrices |
| title_auth | Probability Measures on Semigroups Convolution Products, Random Walks, and Random Matrices |
| title_exact_search | Probability Measures on Semigroups Convolution Products, Random Walks, and Random Matrices |
| title_full | Probability Measures on Semigroups Convolution Products, Random Walks, and Random Matrices by Göran Högnäs, Arunava Mukherjea |
| title_fullStr | Probability Measures on Semigroups Convolution Products, Random Walks, and Random Matrices by Göran Högnäs, Arunava Mukherjea |
| title_full_unstemmed | Probability Measures on Semigroups Convolution Products, Random Walks, and Random Matrices by Göran Högnäs, Arunava Mukherjea |
| title_short | Probability Measures on Semigroups |
| title_sort | probability measures on semigroups convolution products random walks and random matrices |
| title_sub | Convolution Products, Random Walks, and Random Matrices |
| topic | Statistics Mathematics Statistics, general Mathematics, general Mathematik Statistik Halbgruppe (DE-588)4022990-7 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd |
| topic_facet | Statistics Mathematics Statistics, general Mathematics, general Mathematik Statistik Halbgruppe Wahrscheinlichkeitstheorie Wahrscheinlichkeitsmaß |
| url | https://doi.org/10.1007/978-1-4757-2388-5 |
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