Advertisement

Functional Analysis and Its Applications

, Volume 30, Issue 2, pp 90–105 | Cite as

Statistical mechanics of combinatorial partitions, and their limit shapes

  • A. M. Vershik
Article

Keywords

Variational Principle Symmetric Group Young Diagram Occupation Number Limit Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. M. Vershik, Asymptotic Combinatorics and Algebraic Analysis, Proceedings of ICM, Vol. 2, Birkhäuser, Zurich (1995).Google Scholar
  2. 2.
    R. Arratia and S. Tavare, “Limit theorems for combinatorial structures,” Rand. Structure Alg.,3, 321–345 (1992).zbMATHMathSciNetGoogle Scholar
  3. 3.
    B. Fristedt, “The structure of random partitions of large integers,” Trans. Am. Math. Soc.,337, 703–735 (1993).zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    J. Pimtan and R. Aldous, “Brownian bridge asymptotics for random mappings,” Rand. Structure Alg.,5, 487–512 (1994).Google Scholar
  5. 5.
    K. Huang, Statistical Mechanics, John Wiley & Sons, New York-London (1963).zbMATHGoogle Scholar
  6. 6.
    A. Ya. Khinchin, Mathematical Foundations of Quantum Statistics [in Russian], Fizmatlit, Moscow-Leningrad (1951).zbMATHGoogle Scholar
  7. 7.
    G. Freiman, New Analytical Results in Subset-Sum Problems, Combinatorics and Algorithms, Jerusalem (1988).Google Scholar
  8. 8.
    A. M. Vershik, “The limit form of convex integral polygons and related questions,” Funkts. Anal. Prilozhen.,28, No. 1, 17–25 (1994).MathSciNetGoogle Scholar
  9. 9.
    I. Barany, “The limit shape of convex lattice polygons,” Discrete Comput. Geom.,13, 279–295 (1995).zbMATHMathSciNetGoogle Scholar
  10. 10.
    Ya. G. Sinai, “A probabilistic approach to the analysis of the statistics of convex polygonal lines,” Funkts. Anal. Prilozhen.,28, No. 2, 41–48 (1994).zbMATHMathSciNetGoogle Scholar
  11. 11.
    A. M. Vershik, “Statistics of the set of naturals partitions,” in: Probab. Theory Math. Stat., Vol. 2, 683–694, VNU Sci. Press.Google Scholar
  12. 12.
    Yu. Yakubovich, “Asymptotics of random partitions of a set,” Zap. Nauchm. Semin. POMI,223, 227–250 (1995).zbMATHGoogle Scholar
  13. 13.
    G. E. Andrews, The Theory of Partitions, Addison Wesley, London-Amsterdam (1976).Google Scholar
  14. 14.
    C. L. Siegel, Lecture on Advanced Analytic Number Theory, Tata Inst., Bombay (1961).Google Scholar
  15. 15.
    M. Szalay and R. Turan, “On some problems of statistical theory of partitions. I,” Acta Math. Acad. Sci. Hungr.,29, 361–379 (1977).zbMATHMathSciNetCrossRefGoogle Scholar
  16. 16.
    A. M. Vershik and S. V. Kerov, “Asymptotics of maximal and typical dimensionality of irreducible partitions of the symmetric group,” Funkts. Anal. Prilozhen.,19, No. 1, 25–36 (1985).zbMATHMathSciNetGoogle Scholar
  17. 17.
    I. M. Ryzhik and I. S. Gradstein, Tables of Integrals, Sums, Series, and Products [in Russian], 4th ed., Fizmatlit, Moscow (1963).Google Scholar
  18. 18.
    A. M. Vershik and A. A. Shmidt, “Limit measures arising in the asymptotic theory of symmetric groups,” Teor. Verovatn. Primenen.,22, No. 1, 72–88 (1978);23, No. 1, 42–54 (1979).Google Scholar
  19. 19.
    A. M. Vershik, “Statistical sum related to Young diagrams,” Zap. Nauchn. Sem. LOMI,164, 20–29 (1987); English transl. in J. Soviet Math.,47, 2379–2386 (1989).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • A. M. Vershik

There are no affiliations available

Personalised recommendations