| Description |
1 online resource (xviii, 180 pages) : illustrations. |
| Physical Medium |
polychrome |
| Description |
text file |
| Series |
Cambridge - IISc series
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|
Cambridge - IISc series.
|
| Bibliography |
Includes bibliographical references and index. |
| Summary |
"Discusses two current areas of noncommutative mathematics, quantum probability and quantum dynamical systems"-- Provided by publisher |
| Contents |
Cover; Title; Copyright; Dedication; Contents; Preface; Conference photo; Introduction; 1 Independence and Lévy Processes in Quantum Probability; 1.1 Introduction; 1.2 What is Quantum Probability?; 1.2.1 Distinguishing features of classical and quantum probability; 1.2.2 Dictionary 'Classical ₄!Quantum'; 1.3 Why do we Need Quantum Probability?; 1.3.1 Mermin's version of the EPR experiment; 1.3.2 Gleason's theorem; 1.3.3 The Kochen-Specker theorem; 1.4 Infinite Divisibility in Classical Probability; 1.4.1 Stochastic independence; 1.4.2 Convolution. |
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1.4.3 Infinite divisibility, continuous convolution semigroups, and Lévy processes1.4.4 The De Finetti-Lévy-Khintchine formula on (R+, +); 1.4.5 Lévy-Khintchine formulae on cones; 1.4.6 The Lévy-Khintchine formula on (Rd, +); 1.4.7 The Markov semigroup of a Lévy process; 1.4.8 Hunt's formula; 1.5 Lévy Processes on Involutive Bialgebras. |
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1.5.1 Definition of Lévy processes on involutive bialgebras 1.5.2 The generating functional of a Lévy process ; 1.5.3 The Schürmann triple of a Lévy process; 1.5.4 Examples. |
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1.6 Lévy Processes on Compact Quantum Groups and their Markov Semigroups 1.6.1 Compact quantum groups; 1.6.2 Translation invariant Markov semigroups; 1.7 Independences and Convolutions in Noncommutative Probability; 1.7.1 Nevanlinna theory and Cauchy-Stieltjes transforms; 1.7.2 Free convolutions; 1.7.3 A useful Lemma; 1.7.4 Monotone convolutions. |
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1.7.5 Boolean convolutions1.8 The Five Universal Independences; 1.8.1 Algebraic probability spaces; 1.8.2 Classical stochastic independence and the product of probability spaces; 1.8.3 Products of algebraic probability spaces; 1.8.4 Classification of the universal independences; 1.9 Lévy Processes on Dual Groups ; 1.9.1 Dual groups. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Probabilities.
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Probabilities. |
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Quantum theory.
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Quantum theory. |
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Potential theory (Mathematics)
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Potential theory (Mathematics) |
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probability. |
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SCIENCE -- Energy. |
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SCIENCE -- Mechanics -- General. |
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SCIENCE -- Physics -- General. |
| Added Author |
Skalski, Adam, 1978- author.
|
| Other Form: |
Print version: Franz, Uwe. Noncommutative mathematics for quantum systems 9781107148055 (DLC) 2015032903 (OCoLC)919316281 |
| ISBN |
9781316562857 (electronic book) |
|
1316562859 (electronic book) |
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9781316675304 (electronic book) |
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1316675300 (electronic book) |
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9781107148055 |
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1107148057 |
|
