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Negative asymptotic topological dimension, a new condensate, and their relation to the quantized Zipf law

Abstract

We introduce the notion of weight for the asymptotic topological dimension. Planck’s formula for black-body radiation is refined. We introduce the notion of negative asymptotic topological dimension (of hole dimension). The condensate in the hole dimension is applied to the quantized Zipf law for frequency dictionaries (obtained earlier by the author).

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Translated from Matematicheskie Zametki, vol. 80, no. 6, 2006, pp. 856–863.

Original Russian Text Copyright © 2006 by V. P. Maslov.

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Maslov, V.P. Negative asymptotic topological dimension, a new condensate, and their relation to the quantized Zipf law. Math Notes 80, 806–813 (2006). https://doi.org/10.1007/s11006-006-0203-7

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  • DOI: https://doi.org/10.1007/s11006-006-0203-7

Key words

  • asymptotic topological dimension
  • condensate
  • Zipf ’s law
  • Plank’s formula for black-body radiation
  • rank distribution
  • frequency dictionary