Transition from Tracy-Widom to Gaussian fluctuations of extremal eigenvalues of sparse Erdős-Rényi graphs
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Publication:2179601
DOI10.1214/19-AOP1378zbMath1440.05181arXiv1712.03936OpenAlexW3020049990MaRDI QIDQ2179601
Jiaoyang Huang, Benjamin Landon, Horng-Tzer Yau
Publication date: 13 May 2020
Published in: The Annals of Probability (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1712.03936
Extremal problems in graph theory (05C35) Random graphs (graph-theoretic aspects) (05C80) Random matrices (probabilistic aspects) (60B20) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Random matrices (algebraic aspects) (15B52) Density (toughness, etc.) (05C42)
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Cites Work
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- Local spectral statistics of Gaussian matrices with correlated entries
- Delocalization and diffusion profile for random band matrices
- Spectral statistics of Erdős-Rényi graphs. I: Local semicircle law
- Averaging fluctuations in resolvents of random band matrices
- The local semicircle law for a general class of random matrices
- Tracy-Widom distribution for the largest eigenvalue of real sample covariance matrices with general population
- Universality of random matrices with correlated entries
- Random matrices: universality of local eigenvalue statistics
- The spectral edge of some random band matrices
- Universality of random matrices and local relaxation flow
- Universality of sine-kernel for Wigner matrices with a small Gaussian perturbation
- Spectra of graphs
- Rigidity of eigenvalues of generalized Wigner matrices
- Spectral statistics of Erdős-Rényi graphs II: eigenvalue spacing and the extreme eigenvalues
- Local semicircle law and complete delocalization for Wigner random matrices
- Spectral partitioning works: planar graphs and finite element meshes
- A universality result for the smallest eigenvalues of certain sample covariance matrices
- Universality results for the largest eigenvalues of some sample covariance matrix ensembles
- Universality at the edge of the spectrum in Wigner random matrices.
- Isotropic self-consistent equations for mean-field random matrices
- Local law and Tracy-Widom limit for sparse random matrices
- Universality for general Wigner-type matrices
- Universality for random matrix flows with time-dependent density
- Fixed energy universality of Dyson Brownian motion
- Bulk universality for generalized Wigner matrices
- Eigenvector distribution of Wigner matrices
- Random matrices: Universality of local eigenvalue statistics up to the edge
- Edge rigidity and universality of random regular graphs of intermediate degree
- Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices
- Local spectral statistics of the addition of random matrices
- Mesoscopic eigenvalue statistics of Wigner matrices
- Convergence of local statistics of Dyson Brownian motion
- Spectral properties of polynomials in independent Wigner and deterministic matrices
- Largest eigenvalues of sparse inhomogeneous Erdős-Rényi graphs
- The local relaxation flow approach to universality of the local statistics for random matrices
- Isotropic local laws for sample covariance and generalized Wigner matrices
- A new application of random matrices: \(\operatorname{Ext} (C_{\text{red}}^*(F_2))\) is not a group
- Fixed Energy Universality for Generalized Wigner Matrices
- Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs: Diluted regime
- Algorithms, Graph Theory, and the Solution of Laplacian Linear Equations
- Edge universality for deformed Wigner matrices
- Bulk universality of sparse random matrices
- Partitioning Sparse Matrices with Eigenvectors of Graphs
- Expander graphs and their applications
- Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps
- Geometric diffusions as a tool for harmonic analysis and structure definition of data: Multiscale methods
- RANDOM MATRICES WITH SLOW CORRELATION DECAY
- Singularities of Solutions to Quadratic Vector Equations on the Complex Upper Half‐Plane
- Random Graphs
- Spectral norm of random matrices
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