
Large deviations for the largest eigenvalues and eigenvectors of spiked random matrices
We consider matrices formed by a random N× N matrix drawn from the Gauss...
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Stability and dynamical transition of a electrically conducting rotating fluid
In this article, we aim to study the stability and dynamic transition of...
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Phase transitions in semisupervised clustering of sparse networks
Predicting labels of nodes in a network, such as community memberships o...
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Eigenvectors of Deformed Wigner Random Matrices
We investigate eigenvectors of rankone deformations of random matrices ...
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Eigenvalues and Spectral Dimension of Random Geometric Graphs in Thermodynamic Regime
Network geometries are typically characterized by having a finite spectr...
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Negative Representation and Instability in Democratic Elections
Motivated by the troubling rise of political extremism and instability t...
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Phase transition in random contingency tables with nonuniform margins
For parameters n,δ,B, and C, let X=(X_kℓ) be the random uniform continge...
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Eigenvector distribution in the critical regime of BBP transition
In this paper, we study the random matrix model of Gaussian Unitary Ensemble (GUE) with fixedrank (aka spiked) external source. We will focus on the critical regime of the BaikBen ArousPéché (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 rediscovered eigenvectoreigenvalue identity, together with the determinantal point process representation of the GUE minor process with external source.
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