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Negative asymptotic topological dimension, a new condensate, and their relation to the quantized Zipf law. (English. Russian original) Zbl 1137.81022
Math. Notes 80, No. 6, 806-813 (2006); translation from Mat. Zametki 80, No. 6, 856-863 (2006).
The paper comprises a brief note on the work in progress on an attempted revision of probability theory from the point of view of quantum statistics (an expanded presentation can be found in [Russ. J. Math. Phys. 14, 66-95 (2007; Zbl 1325.81111)]). The Author investigates possible foundational links of the quantum statistics (Bose, Fermi, Planck etc. probability laws) with the standard classical event/data series analysis, like e.g. word sequences in literary texts (linguistics), economic foundations for the Zipf law (econo-physics). A number of novel concepts has a clear physical provenance, albeit their usage involves a certain degree of liberty. One needs extended texts (c.f. a reference above) to grasp precise definitions of the negative asymptotic topological dimension, quantization of spaces of negative and positive dimensions, analogies with the notion of (Dirac) holes in quantum physics and the usage of quantum statistics in the linguistic analysis of text complexity.

81S05 Commutation relations and statistics as related to quantum mechanics (general)
82B10 Quantum equilibrium statistical mechanics (general)
60E05 Probability distributions: general theory
54F45 Dimension theory in general topology
65C60 Computational problems in statistics (MSC2010)
62-07 Data analysis (statistics) (MSC2010)
62E20 Asymptotic distribution theory in statistics
62P35 Applications of statistics to physics
Full Text: DOI
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