Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles

DOI10.1007/BF02180200zbMath0916.15009MaRDI QIDQ1285192

Leonid Pastur, Mariya Shcherbina

Publication date: 6 July 1999

Published in: Journal of Statistical Physics (Search for Journal in Brave)

zbMATH Keywords

random matricesquantum field theoryuniversality conjectureeigenvalue statisticslocal asymptotic regimeorthogonal polynomial technique

Mathematics Subject Classification ID

Quantum field theory on lattices (81T25) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Random matrices (algebraic aspects) (15B52) Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable (33C50)

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Cites Work

• Unnamed Item
• Quantum field theory techniques in graphical enumeration
• On the universality of the level spacing distribution for some ensembles of random matrices
• Fredholm determinants, differential equations and matrix models
• Eigenvalue distribution of large random matrices, from one matrix to several coupled matrices
• On the statistical mechanics approach in the random matrix theory: Integrated density of states.
• Universality of the correlations between eigenvalues of large random matrices.
• A Class of Matrix Ensembles