FoCM 2014 conference

Workshop B6 - Random Matrices - Semi-plenary talk

December 17, 17:05 ~ 17:55 - Room B12

New Formulae Relating Finite GOE and LUE --- from Numerical Experiments to Proofs

Folkmar Bornemann

TU München, Germany   -

Gap probabilities of finite-dimensional GOE can be expressed as Pfaffians of single integrals with jump discontinuities that severely bound the effectiveness of quadrature-based numerical methods. Starting from recursive relations with LUE that are either valid in the large matrix limit (due to Metha and Cloizeaux) or hold for every second gap at even dimensions (due to Forrester), we have systematically explored candidates for the "missing" formulae through numerical experiments guided by heuristic arguments. While some of those candidates seem to be exact, other are still surprisingly accurate (and, therefore, probably useful) already for small dimensions even though they are only asymptotically exact. Proving the observed facts is ongoing work.

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