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2006, Relationships between τ-functions and Fredholm determinant expressions for gap probabilities in random matrix theory, Nonlinearity 19
| Citations: | 5 - 1 self |
BibTeX
@MISC{Desrosiers_2006,relationships,
author = {Patrick Desrosiers and Peter and J. Forrester},
title = {2006, Relationships between τ-functions and Fredholm determinant expressions for gap probabilities in random matrix theory, Nonlinearity 19},
year = {}
}
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Abstract
Abstract. The gap probabilities at the hard and soft edges of scaled random matrix ensembles with orthogonal symmetry are known in terms of τ-functions. Extending recent work relating to the soft edge, it is shown that these τ-functions, and their generalizations to contain a generating function like parameter, can be expressed as Fredholm determinants. These same Fredholm determinants also occur in exact expressions for gap probabilities in scaled random matrix ensembles with unitary and symplectic symmetry. 1.
