Transition Distributions of Young Diagrams Under Periodically Weighted Plancherel Measures  

作　　者：Zhong-gen Su 

机构地区：[1]Department of Mathematics, Zhejiang University, Hangzhou 310027, China

出　　处：《Acta Mathematicae Applicatae Sinica》2009年第4期655-674,共20页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(No.10671176)

摘　　要：Kerov[16,17] proved that Wigner＇s semi-circular law in Gauss[an unitary ensembles is the transition distribution of the omega curve discovered by Vershik and Kerov[34] for the limit shape of random partitions under the Plancherel measure. This establishes a close link between random Plancherel partitions and Gauss[an unitary ensembles, In this paper we aim to consider a general problem, namely, to characterize the transition distribution of the limit shape of random Young diagrams under Poissonized Plancherel measures in a periodic potential, which naturally arises in Nekrasov＇s partition functions and is further studied by Nekrasov and Okounkov[25] and Okounkov[28,29]. We also find an associated matrix mode[ for this transition distribution. Our argument is based on a purely geometric analysis on the relation between matrix models and SeibergWitten differentials.Kerov[16,17] proved that Wigner＇s semi-circular law in Gauss[an unitary ensembles is the transition distribution of the omega curve discovered by Vershik and Kerov[34] for the limit shape of random partitions under the Plancherel measure. This establishes a close link between random Plancherel partitions and Gauss[an unitary ensembles, In this paper we aim to consider a general problem, namely, to characterize the transition distribution of the limit shape of random Young diagrams under Poissonized Plancherel measures in a periodic potential, which naturally arises in Nekrasov＇s partition functions and is further studied by Nekrasov and Okounkov[25] and Okounkov[28,29]. We also find an associated matrix mode[ for this transition distribution. Our argument is based on a purely geometric analysis on the relation between matrix models and SeibergWitten differentials.

关 键 词：Limit shape Limiting density of eigenvalues Poissonized Plancherel measures in a periodic potential Transition distributions Unitary invariant matrix models 

分 类 号：O29[理学—应用数学]