We prove large deviations principles for spectral measures of perturbed (or spiked) matrix models in the direction of an eigenvector of the perturbation. In each model under study, we provide two approaches, one of which relying on large deviations principle of unperturbed models derived in the previous work “Sum rules via large deviations” (Gamboa et al. [Sum rules via large deviations, J. Funct. Anal. 270(2) (2016) 509–559]).

中文翻译：

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一些尖峰矩阵的光谱测量的大偏差

我们证明了在扰动特征向量方向上扰动（或尖峰）矩阵模型的光谱测量的大偏差原则。在所研究的每个模型中，我们提供了两种方法，其中一种依赖于之前的工作“通过大偏差求和规则”（Gamboa等人[通过大偏差求和规则，J. Funct。 Anal.  270 (2) (2016) 509–559])。