A quantum-mechanical functional central limit theorem |
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Authors: | AM Cockroft SP Gudder RL Hudson |
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Institution: | Mathematics Department, University of Nottingham, University Park, Nottingham NG7 2RD, England;Mathematics Department, University of Denver USA;Mathematics Department, University of Nottingham, University Park, Nottingham NG7 2RD, England |
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Abstract: | Continuing an earlier work 4], properties of canonical Wiener processes are investigated. An analog of the sample path continuity property is obtained. A noncommutative counterpart of weak convergence is formulated. Operator processes (Pn, Qn) analogous to the random-walk approximating processes of the Donsker invariance principle are defined in terms of a sequence (pi, qi) of pairs of quantum mechanical canonical observables satisfying hypotheses analogous to those of the classical central limit theorem. It is shown that Pn, Qn) converges weakly to a canonical Wiener process. |
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Keywords: | 28-A-40 60-B-10 81-A-20 canonical quantum-mechanics Wiener process functional central limit theorem |
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