特征值分离、BBP跃迁和约束布朗运动
Eigenvalue detachment, BBP transition and constrained Brownian motion
摘要：
我们讨论了本征值分离过渡的尺度波动的路径位于凸边界附近的各种物理性质的合奏。我们认为数值上的BBP（Baik-Ben Arous-Péché）过渡从高斯到Tracy-Widom标度的波动在几个统计系统的正则和微正则系综，并确定相应的控制参数在每种情况下。特别是，对于固定的路径长度（微正则）合奏的路径位于附近的一个部分可渗透的微循环，过渡发生在临界值的渗透率。Tracy-Widom制度和BBP的波动过渡进行了讨论的Jakiw-Teitelbom（JT）重力与径向截止，反过来，有一个解释为一个固定长度的世界线几何约束轨迹的一个带电粒子在一个有效的横向磁场的合奏。
英文摘要：
We discuss the eigenvalue detachment transition in terms of scaling of fluctuations in ensembles of paths located near convex boundaries of various physical nature. We consider numerically the BBP-like (Baik-Ben Arous-Péché) transition from the Gaussian to the Tracy-Widom scaling of fluctuations in several statistical systems for both canonical and microcanonical ensembles and identify the corresponding control parameter in each case. In particular, for fixed path length (microcanonical) ensemble of paths located in the vicinity of a partially permeable semicircle, the transition occurs at the critical value of a permeability. The Tracy-Widom regime and the BBP-like transition for fluctuations are discussed in terms of the Jakiw-Teitelbom (JT) gravity with a radial cutoff which, in turn, has an interpretation as a ensemble of fixed length world-line geometrically constrained trajectories of a charged particle in an effective transversal magnetic field.
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