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Funktsional. Anal. i Prilozhen., 2003, Volume 37, Issue 4, Pages 39–48 (Mi faa167)  

This article is cited in 4 scientific papers (total in 5 papers)

Asymptotics of the Uniform Measures on Simplices and Random Compositions and Partitions

A. M. Vershikab, Yu. V. Yakubovichb

a International Erwin Schrödinger Institute for Mathematical Physics
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: We study the limiting behavior of uniform measures on finite-dimensional simplices as the dimension tends to infinity and a discrete analog of this problem, the limiting behavior of uniform measures on compositions. It is shown that the coordinate distribution of a typical point in a simplex, as well as the distribution of summands in a typical composition with given number of summands, is exponential. We apply these assertions to obtain a more transparent proof of our result on the limit shape of partitions with given number of summands, refine the estimate on the number of summands in partitions related to a theorem by Erdős and Lehner about the asymptotic absence of repeated summands, and outline the proof of the sharpness of this estimate.

Keywords: limit shape, composition, partition, uniform measure on a simplex

DOI: https://doi.org/10.4213/faa167

Full text: PDF file (163 kB)
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English version:
Functional Analysis and Its Applications, 2003, 37:4, 273–280

Bibliographic databases:

UDC: 519.214
Received: 15.09.2003

Citation: A. M. Vershik, Yu. V. Yakubovich, “Asymptotics of the Uniform Measures on Simplices and Random Compositions and Partitions”, Funktsional. Anal. i Prilozhen., 37:4 (2003), 39–48; Funct. Anal. Appl., 37:4 (2003), 273–280

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. V. Yakubovich, “On the coincidence of limit shapes for integer partitions and compositions, and a slicing of Young diagrams”, J. Math. Sci. (N. Y.), 131:2 (2005), 5569–5577  mathnet  crossref  mathscinet  zmath  elib  elib
    2. Erlihson, MM, “Limit shapes of Gibbs distributions on the set of integer partitions: The expansive case”, Annales de l Institut Henri Poincare-Probabilites et Statistiques, 44:5 (2008), 915  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. F. Petrov, “Limits shapes of Young diagrams. Two elementary approaches”, J. Math. Sci. (N. Y.), 166:1 (2010), 63–74  mathnet  crossref
    4. Eriksson K. Sjostrand J., “Limiting Shapes of Birth-and-Death Processes on Young Diagrams”, Adv. Appl. Math., 48:4 (2012), 575–602  crossref  mathscinet  zmath  isi  elib  scopus
    5. V. M. Buchstaber, M. I. Gordin, I. A. Ibragimov, V. A. Kaimanovich, A. A. Kirillov, A. A. Lodkin, S. P. Novikov, A. Yu. Okounkov, G. I. Olshanski, F. V. Petrov, Ya. G. Sinai, L. D. Faddeev, S. V. Fomin, N. V. Tsilevich, Yu. V. Yakubovich, “Anatolii Moiseevich Vershik (on his 80th birthday)”, Russian Math. Surveys, 69:1 (2014), 165–179  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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