Quantum Probability And Related Topics: Qp-pq (Volume Vi)

This volume contains several surveys of important developments in quantum probability.\n\nThe 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 ?-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.Quantum Probability And Related Topics: Qp-pq (Volume Vi) is written by Accardi Luigi and published by World Scientific. ISBNs for Quantum Probability And Related Topics: Qp-pq (Volume Vi) are 9789814360203, 9814360201 and the print ISBNs are 9789810206802, 9810206801.