Gaussian fluctuations of Jack-deformed random Young diagrams

• 成果类型: Article
• 署名作者: Dolega, Maciej; Sniady, Piotr
• 署名单位: Adam Mickiewicz University; University of Wroclaw; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-018-0854-9
• 发表日期: 2019
• 页码: 133-176
• 关键词: characters

摘要

We introduce a large class of random Young diagrams which can be regarded as a natural one-parameter deformation of some classical Young diagram ensembles; a deformation which is related to Jack polynomials and Jack characters. We show that each such a random Young diagram converges asymptotically to some limit shape and that the fluctuations around the limit are asymptotically Gaussian.