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• W2068561107 abstract "In a two-state free probability space ( A , φ , ψ ) , we define an algebraic two-state free Brownian motion to be a process with two-state freely independent increments whose two-state free cumulant generating function R φ , ψ ( z ) is quadratic. Note that a priori, the distribution of the process with respect to the second state ψ is arbitrary. We show, however, that if A is a von Neumann algebra, the states φ , ψ are normal, and φ is faithful, then there is only a one-parameter family of such processes. Moreover, with the exception of the actual free Brownian motion (corresponding to φ = ψ ), these processes only exist for finite time." @default.
• W2068561107 created "2016-06-24" @default.
• W2068561107 creator A5083519878 @default.
• W2068561107 date "2011-01-01" @default.
• W2068561107 modified "2023-09-29" @default.
• W2068561107 title "Two-state free Brownian motions" @default.
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• W2068561107 doi "https://doi.org/10.1016/j.jfa.2010.09.004" @default.
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