A note on spiked Wishart matrices. (English) Zbl 1380.60014
Summary: Consider the spiked complex Wishart matrices with sample size \(M\) and population size \(N\). As \(N, M \rightarrow \infty\) such that \(N/M \rightarrow \gamma \in(0,1]\), J. Baik et al. [Ann. Probab. 33, No. 5, 1643–1697 (2005; Zbl 1086.15022)] established a phase transition of the largest eigenvalue. In this paper we show that some of their main results also hold true in the case where \(N/M \rightarrow 0\). More precisely, we prove that limiting distribution of the largest eigenvalue is the finite GUE distribution.
Citations:
Zbl 1086.15022References:
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