LIMIT SHAPES FOR GROWING EXTREME CHARACTERS OF U(∞)

• 成果类型: Article
• 署名作者: Borodin, Alexei; Bufetov, Alexey; Olshanski, Grigori
• 署名单位: Massachusetts Institute of Technology (MIT); Kharkevich Institute for Information Transmission Problems of the RAS; Russian Academy of Sciences; HSE University (National Research University Higher School of Economics)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1050
• 发表日期: 2015
• 页码: 2339-2381
• 关键词: dimensional unitary-group; plancherel measure; symmetrical group; young-diagrams; REPRESENTATIONS; asymptotics

摘要

We prove the existence of a limit shape and give its explicit description for certain probability distribution on signatures (or highest weights for unitary groups). The distributions have representation theoretic origin-they encode decomposition on irreducible characters of the restrictions of certain extreme characters of the infinite-dimensional unitary group U (infinity) to growing finite-dimensional unitary subgroups U (N). The characters of U(infinity) are allowed to depend on N. In a special case, this describes the hydrodynamic behavior for a family of random growth models in (2 + 1)-dimensions with varied initial conditions.