2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66957Consider random Young diagrams with a fixed number n of boxes, where the probability distribution on diagrams is determined by the Plancherel measure. That is, the weight of a diagram is proportional to the squared dimension of the corresponding irreducible representation of the symmetric group S_n. As n goes to infinity, the boundary of the (suitably scaled) random diagram concentrates near a curve Omega (Logan-Shepp 1977, Vershik-Kerov 1977). In 1993, Kerov announced a central limit theorem describing Gaussian fluctuations of random diagrams around the limit shape Omega. Here we propose a reconstruction of his proof, largely based on Kerov's unpublished work notes (1999). We also discuss a striking similarity between Kerov's result and central limit theorems for random matrices (Diaconis-Shahshahani, Johansson).AMS-TeX, 49 pages, no figuresCombinatoricsProbabilityRepresentation Theory05E05 (Primary) 05E10, 20C30, 20C32, 60B10, 60B15 (Secondary)text