Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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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