Correlation functions, cluster functions, and spacing distributions for random matrices
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Publication:1806406
DOI10.1023/A:1023084324803zbMATH Open0942.60099arXivsolv-int/9804004WikidataQ56950682 ScholiaQ56950682MaRDI QIDQ1806406
Author name not available (Why is that?)
Publication date: 21 August 2000
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/solv-int/9804004
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