| Quantum Probability and Related Topics: Qp-Pq (Volume VI) Contributor(s): Accardi, Luigi (Editor) |
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ISBN: 9810206801 ISBN-13: 9789810206802 Publisher: World Scientific Publishing Company OUR PRICE: $182.40 Product Type: Hardcover - Other Formats Published: October 1991 |
| Additional Information |
| BISAC Categories: - Mathematics | Probability & Statistics - General - Science | Physics - Quantum Theory - Science | Physics - Mathematical & Computational |
| Dewey: 530.12 |
| LCCN: 92024406 |
| Series: Qp-Pq: Quantum Probability and White Noise Analysis |
| Physical Information: 1.3" H x 6.2" W x 8.8" (1.90 lbs) 532 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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 ϖ-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. |