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 -