Fluctuations at the edges of the spectrum of the full rank deformed GUE

• 成果类型: Article
• 署名作者: Capitaine, Mireille; Peche, Sandrine
• 署名单位: Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-015-0628-6
• 发表日期: 2016
• 页码: 117-161
• 关键词: largest eigenvalue; free convolution; RANDOM MATRICES; UNIVERSALITY; pearcey; deformations

摘要

We consider a full rank deformation of the GUE where is a full rank Hermitian matrix of size and is a GUE. The empirical eigenvalue distribution of converges to a probability distribution . We identify all the possible limiting eigenvalue statistics at the edges of the spectrum, including outliers, edges and merging points of connected components of the limiting spectrum. The results are stated in terms of a deterministic equivalent of the empirical eigenvalue distribution of , namely the free convolution of the semi-circle distribution and the empirical eigenvalues distribution of A(N).