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A local limit theorem for random strict partitions. / Freiman, G; Vershik, AM; Yakubovich, YV.
в: Theory of Probability and its Applications, Том 44, № 3, 1999, стр. 453-468.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - A local limit theorem for random strict partitions
AU - Freiman, G
AU - Vershik, AM
AU - Yakubovich, YV
PY - 1999
Y1 - 1999
N2 - We consider a set of partitions of natural number n on distinct summands with uniform distribution. We investigate the limit shape of the typical partition as n --> infinity, which was found in [A. M. Vershik, Funct. Anal. Appl., 30 (1996), pp. 90-105], and fluctuations of partitions near its limit shape. The geometrical language we use allows us to reformulate the problem in terms of random step functions (Young diagrams). We prove statements of local limit theorem type which imply that joint distribution of fluctuations in a number of points is locally asymptotically normal. The proof essentially uses the notion of a large canonical ensemble of partitions.
AB - We consider a set of partitions of natural number n on distinct summands with uniform distribution. We investigate the limit shape of the typical partition as n --> infinity, which was found in [A. M. Vershik, Funct. Anal. Appl., 30 (1996), pp. 90-105], and fluctuations of partitions near its limit shape. The geometrical language we use allows us to reformulate the problem in terms of random step functions (Young diagrams). We prove statements of local limit theorem type which imply that joint distribution of fluctuations in a number of points is locally asymptotically normal. The proof essentially uses the notion of a large canonical ensemble of partitions.
KW - partition
KW - Young diagram
KW - large ensemble of partitions
KW - local limit theorem
M3 - статья
VL - 44
SP - 453
EP - 468
JO - Theory of Probability and its Applications
JF - Theory of Probability and its Applications
SN - 0040-585X
IS - 3
ER -
ID: 11511614