Infinite wedge and random partitions
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We use representation theory to obtain a number of exact results for random partitions. In particular, we prove a simple determinantal formula for correlation functions of what we call the Schur measure on partitions (which is a far reaching generalization of the Plancherel measure; see , ) and also observe that these correlations functions are \( \tau \)-functions for the Toda lattice hierarchy. We also give a new proof of the formula due to Bloch and the author  for the so-called n-point functions of the uniform measure on partitions and comment on the local structure of a typical partition.