Titlebook: Quantum Potential Theory; Philippe Biane,Luc Bouten,Quanhua Xu,Uwe Franz,Mic Book 2008 Springer-Verlag Berlin Heidelberg 2008 Dirichlet fo

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Book 2008ry and it quantum analogs, i.e. quantum Markov processes and semigroups, quantum random walks, Dirichlet forms on C* and von Neumann algebras, and boundary theory. Applications to quantum physics, in particular the filtering problem in quantum optics, are also presented..

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0075-8434 eory: Structure and Applications to Physics," held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald from February 26 to March 10, 2007...Quantum potential theory studies noncommutative (or quantum) analogs of classical potential theory. These lectures provide an introduction to this theory, co

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Lecture Notes in Mathematicshttp://image.papertrans.cn/q/image/781423.jpg

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Potential Theory in Classical Probability,These notes are an elementary introduction to classical potential theory and to its connection with probabilistic tools such as stochastic calculus and the Markov property. In particular we review the probabilistic interpretations of harmonicity, of the Dirichlet problem, and of the Poisson equation using Brownian motion and stochastic calculus.

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Introduction to Random Walks on Noncommutative Spaces,We introduce several examples of random walks on noncommutative spaces and study some of their probabilistic properties. We emphasize connections between classical potential theory and group representations.

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Philippe Biane,Luc Bouten,Quanhua Xu,Uwe Franz,MicIncludes supplementary material: