Mathematical Notes

, Volume 80, Issue 5–6, pp 806–813 | Cite as

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

  • V. P. Maslov


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).

Key words

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


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  1. 1.
    V. P. Maslov, “Quantum linguistic statistics,” Russ. J. Math. Phys., 13 (2006), no. 3, 315–325.CrossRefGoogle Scholar
  2. 2.
    V. P. Maslov and T. V. Maslova, “On Zipf’s law and rank distributions in linguistics and semiotics,” Mat. Zametki [Math. Notes], 80 (2006), no. 5, 718–732.Google Scholar
  3. 3.
    V. P. Maslov, “On the minimization of the statistical risk of purchases on the housing market and of durable goods,” Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.], 411 (2006), no. 6.Google Scholar
  4. 4.
    V. P. Maslov, “Phase transitions of the zeroth kind and the quantization of Zipf’s law,” Teoret. Mat. Fiz. [Theoret. and Math. Phys.], 150 (2007), no. 1, 121–141.Google Scholar
  5. 5.
    V. P. Maslov, “Nonlinear mean in economics,” Mat. Zametki [Math. Notes], 78 (2005), no. 3, 377–395.MathSciNetGoogle Scholar
  6. 6.
    V. P. Maslov, “On a general theorem of set theory resulting in the Gibbs, Bose-Einstein, and Pareto distributions and the Zipf-Mandelbrot law for stock market,” Mat. Zametki [Math. Notes], 78 (2005), no. 6, 870–877.MathSciNetGoogle Scholar
  7. 7.
    V. P. Maslov, “The lack-of-preference law and the corresponding distributions in frequency probability theory,” Mat. Zametki [Math. Notes], 80 (2006), no. 2, 220–230.Google Scholar
  8. 8.
    M. Gromov, “Asymptotic invariants of infinite groups,” in: Geometric Group Theory, vol. 2 (Sussex, 1991), London Math. Soc. Lecture Note Ser., vol. 182, Cambridge Univ. Press, Cambridge, 1993, pp. 1–295.Google Scholar
  9. 9.
    A. Dranishnikov and J. Smith, “Asymptotic dimension of discrete groups,” in: arXiv: math.GT/0603055v1 (2 Mar 2006).Google Scholar
  10. 10.
    L. D. Landau and E. M. Lifshits, Theoretical Physics, vol. 5, Statistical Physics [in Russian], Nauka, Moscow, 1976.Google Scholar
  11. 11.
    O. Viro, “Dequantization of real algebraic geometry on logarithmic paper,” in: 3rd European Congress of Mathematics, vol. I (Barcelona, 2000), Progr. Math., vol. 201, Birkhäuser, Basel, 2001, pp. 135–146.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • V. P. Maslov
    • 1
  1. 1.M. V. Lomonosov Moscow State UniversityRussia

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