A new approach to derive Pfaffian structures for random matrix ensembles

DOI10.1088/1751-8113/43/13/135204zbMath1188.81080arXiv0912.0658OpenAlexW1977947775MaRDI QIDQ3553661

Thomas Guhr, Mario Kieburg

Publication date: 21 April 2010

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.0658

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Pfaffian systems (58A17) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Supersymmetry and quantum mechanics (81Q60) Random matrices (algebraic aspects) (15B52) Statistical mechanics of nanostructures and nanoparticles (82D80)

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Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence ⋮ Bures–Hall ensemble: spectral densities and average entropies ⋮ Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case ⋮ The Ginibre evolution in the large-N limit ⋮ GUE-chGUE transition preserving chirality at finite matrix size ⋮ Relating the Bures measure to the Cauchy two-matrix model ⋮ Preserving topology while breaking chirality: from chiral orthogonal to anti-symmetric Hermitian ensemble ⋮ On random matrix averages involving half-integer powers of GOE characteristic polynomials ⋮ Asymptotic coincidence of the statistics for degenerate and non-degenerate correlated real Wishart ensembles

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