dorsal/arxiv
View SchemaCorrelation Functions, Cluster Functions and Spacing Distributions for Random Matrices
| Authors | Craig A. Tracy, Harold Widom |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9804004 |
| URL | https://arxiv.org/abs/solv-int/9804004 |
| DOI | 10.1023/A:1023084324803 |
| Journal | J. Statistical Physics 92 (1998), 809-835. |
Abstract
The usual formulas for the correlation functions in orthogonal and symplectic matrix models express them as quaternion determinants. From this representation one can deduce formulas for spacing probabilities in terms of Fredholm determinants of matrix-valued kernels. The derivations of the various formulas are somewhat involved. In this article we present a direct approach which leads immediately to scalar kernels for unitary ensembles and matrix kernels for the orthogonal and symplectic ensembles, and the representations of the correlation functions, cluster functions and spacing distributions in terms of them.
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"abstract": "The usual formulas for the correlation functions in orthogonal and symplectic\nmatrix models express them as quaternion determinants. From this representation\none can deduce formulas for spacing probabilities in terms of Fredholm\ndeterminants of matrix-valued kernels. The derivations of the various formulas\nare somewhat involved. In this article we present a direct approach which leads\nimmediately to scalar kernels for unitary ensembles and matrix kernels for the\northogonal and symplectic ensembles, and the representations of the correlation\nfunctions, cluster functions and spacing distributions in terms of them.",
"arxiv_id": "solv-int/9804004",
"authors": [
"Craig A. Tracy",
"Harold Widom"
],
"categories": [
"solv-int",
"math.SP",
"nlin.SI"
],
"doi": "10.1023/A:1023084324803",
"journal_ref": "J. Statistical Physics 92 (1998), 809-835.",
"title": "Correlation Functions, Cluster Functions and Spacing Distributions for Random Matrices",
"url": "https://arxiv.org/abs/solv-int/9804004"
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