Random matrix ensembles associated to compact symmetric spaces
| Autor: | Eduardo Dueñez |
|---|---|
| Rok vydání: | 2001 |
| Předmět: |
Pure mathematics
010102 general mathematics Mathematical analysis FOS: Physical sciences Statistical and Nonlinear Physics Unitary matrix Mathematical Physics (math-ph) 53C35 33C45 (Secondary) 01 natural sciences 15A52 (Primary) Compact space Unit circle Unitary group Symmetric space 0103 physical sciences 010307 mathematical physics 0101 mathematics Circular ensemble Random matrix Mathematical Physics Symplectic geometry Mathematics |
| DOI: | 10.48550/arxiv.math-ph/0111005 |
| Popis: | We introduce random matrix ensembles that correspond to the infinite families of irreducible Riemannian symmetric spaces of type I. In particular, we recover the Circular Orthogonal and Symplectic Ensembles of Dyson, and find other families of (unitary, orthogonal and symplectic) ensembles of Jacobi type. We discuss the universal and weakly universal features of the global and local correlations of the levels in the bulk and at the hard edge of the spectrum (i.e., at the "central points" +/-1 on the unit circle). Previously known results are extended, and we find new simple formulas for the Bessel Kernels that describe the local correlations around a central point. Comment: 41 pages, 3 figures, LaTeX 2e. Introduction rewritten to include statements of main results. To appear in CMP |
| Databáze: | OpenAIRE |
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