A local limit theorem for random strict partitions (Q2711136)

The authors consider a set of partitions of a natural number \(n\) on distinct summands with uniform distribution. They investigate the limit shape of the typical partition as \(n\to\infty\), which was found by \textit{A. M. Vershik} [Funct. Anal. Appl. 30, 90--105 (1996); translation from Funkts. Anal. Prilozh. 30, No. 2, 19--39 (1996; Zbl 0868.05004)], and fluctuations of partitions near its limit shape. The geometrical language allows him to reformulate the problem in terms of random step functions (Young diagrams). They 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.