2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78849Using techniques from integrable systems, we obtain a number of exact results for random partitions. In particular, we prove a simple formula for correlation functions of what we call the Schur measure on partitions (which is a far reaching generalization of the Plancherel measure, see math.CO/9905032) and also show that these correlations functions are tau-functions for the Toda lattice hierarchy. Also we give a new proof of the formula due to Bloch and the author, see alg-geom/9712009, for the so called n-point functions of the uniform measure on partitions and comment on the local structure of a typical partition.LaTeX, 29 pagesRepresentation TheoryMathematical PhysicsCombinatoricsProbabilitytext