Asymptotic analysis of random partitions ∗
نویسندگان
چکیده
In this paper we aim to review some works on the asymptotic behaviors of random partitions. The focus is upon two basic probability models— uniform partitions and Plancherel partitions. One of fundamental results is the existence of limit shapes, which corresponds to the classic law of large numbers. The fluctuations around the limit shape are also considered; the well-known Gumbel distribution, Tracy-Widom distribution and normal distribution will be used to describe the asymptotic fluctuations at the edge and in the bulk of the spectrum of random partitions. The technique used in asymptotic analysis is the so-called poissonization and depoissonization method, a peculiar conditioning argument. We are content with describing some basic facts and remarkable results; no complete proof is given.
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