论文标题
BBP过渡的关键状态中的特征向量分布
Eigenvector distribution in the critical regime of BBP transition
论文作者
论文摘要
在本文中，我们研究了具有固定级（又名尖刺）外源的高斯单位合奏（GUE）的随机矩阵模型。我们将重点关注Baik-Ben唤醒的临界（BBP）相变的关键状态，并建立与领先特征值相关的特征向量的分布。该分布是根据延长的通风内核的确定点过程给出的。我们的结果可以视为BBP特征值相变（Arxiv：Math/0403022）的特征向量对应物。分布的推导利用了最近重新发现的特征向量 - 元素价值身份，以及带有外部源的Gue Minor过程的确定点过程表示。
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-Péché (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.
