The matrix Dyson equation and its applications for random matrices

zbMath1443.15001arXiv1903.10060MaRDI QIDQ5217140

László Erdős

Publication date: 21 February 2020

Full work available at URL: https://arxiv.org/abs/1903.10060

zbMATH Keywords

random matrixTracy-Widom distributionlocal semicircle lawDyson Brownian motionDyson sine kernelmatrix Dyson equationWigner-Dyson-Mehta conjecture

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Random matrices (algebraic aspects) (15B52) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to linear algebra (15-01)

Related Items (6)

Large deviations for the largest eigenvalue of matrices with variance profiles ⋮ KPZ-type fluctuation exponents for interacting diffusions in equilibrium ⋮ Central limit theorem for linear spectral statistics of block-Wigner-type matrices ⋮ Proof methods in random matrix theory ⋮ Single eigenvalue fluctuations of general Wigner-type matrices ⋮ Anomalous singularity of the solution of the vector Dyson equation in the critical case

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