In this paper, we study the random matrix model of Gaussian Unitary Ensemble (GUE) with fixed-rank (aka spiked) external source. We will focus on the critical regime of the Baik-Ben Arous-P\'ech\'e (BBP) phase transition and establish the distribution of the eigenvectors associated with the leading eigenvalues. The distribution is given in terms of a determinantal point process with extended Airy kernel. Our result can be regarded as an eigenvector counterpart of the BBP eigenvalue phase transition (arXiv:math/0403022). The derivation of the distribution makes use of the recently re-discovered eigenvector-eigenvalue identity, together with the determinantal point process representation of the GUE minor process with external source.

翻译：在本文中,我们研究了具有固定(卡加加)外部源的高森单体组合(GUE)随机矩阵模型,我们将侧重于Baik-Ben Aurous-P\'ech\'e(BBP)阶段过渡的关键机制,并确定与主要源值相关的源的分布。该分布以扩展空气内核的确定点过程为根据。我们的结果可以被视为BBPP的源值阶段过渡(arXiv:math/0403022)的替代方。该分布的衍生利用了最近重新发现的源值-源值特性,以及GUE次要过程与外部来源的确定点过程。