2006/04/30 by Patrick Desrosiers, Peter J. Forrester, Peter J Forrester · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Random Matrices and Applications #math-ph #math.MP #msc:15A52 #msc:34M55 #msc:45B05 #nlin.SI
paper · pdf · doi:10.1088/0951-7715/19/7/012
published as 2006 Nonlinearity 19 1643-1656 · 16 pages, amstex; (v2) published version, some equations corrected
openalex publication_date 2006/06/19 · arxiv created 2006/07/04 · arxiv updated 2012/08/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
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 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.