Abstract:
An example of noncommutative Brownian motion is constructed on the monotone Fock space which is a kind of “Fock space” generated by all the decreasing finite sequences of positive real numbers. The probability distribution at time associated to this Brownian motion is shown to be the arcsine law normalized to mean 0 and variance t.
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Received: 15 March 1996\,/\,Accepted: 2 July 1996
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Muraki, N. Noncommutative Brownian Motion in Monotone Fock Space . Comm Math Phys 183, 557–570 (1997). https://doi.org/10.1007/s002200050043
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DOI: https://doi.org/10.1007/s002200050043