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Asymptotics of the uniform measures on simplices and random compositions and partitions. / Vershik, A. M.; Yakubovich, Yu V.

в: Functional Analysis and its Applications, Том 37, № 4, 01.10.2003, стр. 273-280.

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Vershik, A. M. ; Yakubovich, Yu V. / Asymptotics of the uniform measures on simplices and random compositions and partitions. в: Functional Analysis and its Applications. 2003 ; Том 37, № 4. стр. 273-280.

BibTeX

@article{6eaf9082263b483e9ea1ef4989d9b77d,
title = "Asymptotics of the uniform measures on simplices and random compositions and partitions",
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 Erd os and Lehner about the asymptotic absence of repeated summands, and outline the proof of the sharpness of this estimate.",
keywords = "Composition, Limit shape, Partition, Uniform measure on a simplex",
author = "Vershik, {A. M.} and Yakubovich, {Yu V.}",
year = "2003",
month = oct,
day = "1",
doi = "10.1023/B:FAIA.0000015578.02338.0e",
language = "English",
volume = "37",
pages = "273--280",
journal = "Functional Analysis and its Applications",
issn = "0016-2663",
publisher = "Springer Nature",
number = "4",

}

RIS

TY - JOUR

T1 - Asymptotics of the uniform measures on simplices and random compositions and partitions

AU - Vershik, A. M.

AU - Yakubovich, Yu V.

PY - 2003/10/1

Y1 - 2003/10/1

N2 - 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 Erd os and Lehner about the asymptotic absence of repeated summands, and outline the proof of the sharpness of this estimate.

AB - 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 Erd os and Lehner about the asymptotic absence of repeated summands, and outline the proof of the sharpness of this estimate.

KW - Composition

KW - Limit shape

KW - Partition

KW - Uniform measure on a simplex

UR - http://www.scopus.com/inward/record.url?scp=3543028678&partnerID=8YFLogxK

U2 - 10.1023/B:FAIA.0000015578.02338.0e

DO - 10.1023/B:FAIA.0000015578.02338.0e

M3 - Article

AN - SCOPUS:3543028678

VL - 37

SP - 273

EP - 280

JO - Functional Analysis and its Applications

JF - Functional Analysis and its Applications

SN - 0016-2663

IS - 4

ER -

ID: 32734562