Asymptotics of Plancherel-type random partitions

JOURNAL OF ALGEBRA

卷:313

Article

Borodin, Alexei ; Olshanski, Grigori

关键词: Plancherel measure;    random partitions;    determinantal processes;    correlation kernel;   

DOI  :  10.1016/j.jalgebra.2006.10.039

来源: Elsevier

【 摘 要 】

We present a solution to a problem suggested by Philippe Biane: we prove that a certain Plancherel-type probability distribution on partitions converges, as partitions get large, to a new determinantal random point process on the set Z(+) of nonnegative integers. This can be viewed as an edge limit transition. The limit process is determined by a correlation kernel on Z(+) which is expressed through the Hermite polynomials, we call it the discrete Hermite kernel. The proof is based on a simple argument which derives convergence of correlation kernels from convergence of unbounded self-adjoint difference operators. Our approach can also be applied to a number of other probabilistic models. As an example, we discuss a bulk limit for one more Plancherel-type model of random partitions. (c) 2007 Elsevier Inc. All fights reserved.

【 授权许可】

Free