Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case

DOI10.1063/5.0164352arXiv2306.12051OpenAlexW4388224245MaRDI QIDQ6064802

Omri Gat, Thomas Guhr, Mario Kieburg, Nico Hahn

Publication date: 11 December 2023

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

Full work available at URL: https://arxiv.org/abs/2306.12051

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52)

Cites Work

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• Bulk and boundary invariants for complex topological insulators. From \(K\)-theory to physics
• A real quaternion spherical ensemble of random matrices
• A short proof of stability of topological order under local perturbations
• Bulk-boundary correspondence for disordered free-fermion topological phases
• The characteristic polynomial of a random unitary matrix and Gaussian multiplicative chaos -- the \(L^2\)-phase
• The characteristic polynomial of a random unitary matrix: a probabilistic approach
• The probability that a random real Gaussian matrix has \(k\) real eigenvalues, related distributions, and the circular law
• Autocorrelation of random matrix polynomials
• Pfaffian point process for the Gaussian real generalised eigenvalue problem
• The characteristic polynomial of a random matrix
• Averages of products and ratios of characteristic polynomials in polynomial ensembles
• Symmetry classes of disordered fermions
• A short course on topological insulators. Band structure and edge states in one and two dimensions
• Moments of the characteristic polynomial in the three ensembles of random matrices
• Complexity of Random Energy Landscapes, Glass Transition, and Absolute Value of the Spectral Determinant of Random Matrices
• An induced real quaternion spherical ensemble of random matrices
• Dyson’s correlation functions and graded symmetry
• Averages of characteristic polynomials in random matrix theory
• General eigenvalue correlations for the real Ginibre ensemble
• A new approach to derive Pfaffian structures for random matrix ensembles
• Derivation of an eigenvalue probability density function relating to the Poincaré disk
• Periodic table for topological insulators and superconductors
• An exact formula for general spectral correlation function of random Hermitian matrices
• Kac–Rice fixed point analysis for single- and multi-layered complex systems
• Skew-orthogonal Laguerre polynomials for chiral real asymmetric random matrices
• Winding number statistics of a parametric chiral unitary random matrix ensemble*
• Derivation of determinantal structures for random matrix ensembles in a new way
• Statistical Ensembles of Complex, Quaternion, and Real Matrices
• Particle–hole symmetries in condensed matter
• Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence

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