This volume contains several surveys of important developments in quantum probability. The new type of quantum central limit theorems, based on the notion of free independence rather than the usual Boson or Fermion independence is discussed. A surprising result is that the role of the Gaussian for this new type of independence is played by the Wigner distribution. This motivated the introduction of new type of quantum independent increments noise, the free noise and the corresponding stochastic calculus. A further generalization, the q-noises, is discussed. The free stochastic calculus is shown to be able to fit naturally into the general representation free calculus. The basic free are shown to be realized as non-adapted stochastic integrals with respect to the usual Boson white noises. Quantum noise on the finite difference algebra is expressed in terms of the usual Boson white noises. A new quantum way of looking at classical stochastic flows, in particular diffusions on Riemannian Manifolds is explained. Quantum groups are discussed from the point of view of possible applications to quantum probability. The applications of quantum probability to physics are surveyed.
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The problem of constructing a satisfactory theory of the irreversible and dissipative quantum phenomena has a long history. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Hopf-von Neumann, Centro Matematico, Springer Verlag, Kyoto Univ, Nuovo Cimento, Academic Press, Dang Ngoc, Theorem Let, Cambridge Philos, Fermion Ito, Kodai Math, Proof of Lemma, Proposition Let, Rhode Island, University of Rome, Vienna Preprint, World Scientific New!
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The problem of constructing a satisfactory theory of the irreversible and dissipative quantum phenomena has a long history. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Hopf-von Neumann, Centro Matematico, Springer Verlag, Kyoto Univ, Nuovo Cimento, Academic Press, Dang Ngoc, Theorem Let, Cambridge Philos, Fermion Ito, Kodai Math, Proof of Lemma, Proposition Let, Rhode Island, University of Rome, Vienna Preprint, World Scientific New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
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This book cites 32
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34
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- Stochastic Differential Equations 1976: Kyoto: International Symposium Proceedings by Kiyosi Ito on page 108, page 283, and page 284
- Probabilistic Properties of Deterministic Systems by Andrzej Lasota on page 451, and page 514
- Ergodic Theory (Grundlehren der mathematischen Wissenschaften) by I. P. Kornfeld on page 192, and page 514
- Operator Algebras and Quantum Statistical Mechanics 1 by Ola Bratteli on page 323, and page 450
- Hopf Algebras (Cambridge Tracts in Mathematics) by Eiichi Abe on page 354
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- Quantum Probability & Related Topics (Qp-Pq, Vol 9) (v. 9) by L. Accardi on 9 pages
- Quantum Probability and Infinite-Dimensional Analysis: Proceedings of the Conference, Burg (Spreewald), Germany, 15-20 March 2001 (Qptpq Quantum Probability and White Noise Analysis, 15) by W. Freudenberg on 6 pages
- Quantum Probability and Related Topics by L. Accardi on 4 pages
- Quantum Interacting Particle Systems: Lecture Notes of the Volterra-Cirm International School, Trento, Italy, 23-29 September 2000 (Qp-Pq, Quantum Probability and White Noise Analysis, V. 14) by Franco Fagnola in Front Matter (1), Front Matter (2), and page 193
- The Semicircle Law, Free Random Variables and Entropy (Mathematical Surveys and Monographs) by Fumio Hiai and Denes Petz in Back Matter (1), Back Matter (2), and Back Matter (3)
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