UID:
almahu_9949880884002882
Format:
1 online resource (226 pages)
Edition:
1st ed.
ISBN:
9789819751730
Series Statement:
KIAS Springer Series in Mathematics Series ; v.3
Note:
Intro -- Preface -- Acknowledgements -- Contents -- 1 Introduction -- Part I GinUE -- 2 Eigenvalue PDFs and Correlations -- 2.1 Eigenvalue PDF -- 2.2 Correlation Functions -- 2.3 Elliptic GinUE -- 2.4 Induced GinUE -- 2.5 Complex Spherical Ensemble -- 2.6 Sub-block of a Unitary Matrix -- 2.7 Products of Complex Ginibre Matrices -- 2.8 Products of Truncated Unitary Matrices -- 2.9 The Distribution of the Squared Eigenvalue Moduli -- 3 Fluctuation Formulas -- 3.1 Counting Function in General Domains -- 3.1.1 Counting Function in a Disk and Scaled Asymptotics -- 3.1.2 Counting Function in the Infinite System -- 3.2 Smooth Linear Statistics -- 3.3 Spatial Modelling and the Thinned GinUE -- 4 Coulomb Gas Model, Sum Rules and Asymptotic Behaviours -- 4.1 Asymptotics Associated with the Configuration Integral -- 4.2 Sum Rules and Asymptotics for the Edge Density -- 4.3 Sum Rules and Asymptotics for the Two- and Higher-Point Correlations -- 5 Normal Matrix Models -- 5.1 Eigenvalue PDF -- 5.2 Equilibrium Measure -- 5.3 Partition Functions -- 5.4 Correlation Functions and Universality -- 6 Further Theory and Applications -- 6.1 Fermi Gas Wave Function Interpretation -- 6.2 Quantum Chaos Applications -- 6.3 Singular Values -- 6.4 Eigenvectors -- 6.5 Non-Hermitian Wigner Ensembles -- Part II GinOE and GinSE -- 7 Eigenvalue Statistics for GinOE and Elliptic GinOE -- 7.1 Eigenvalue PDF for GinOE -- 7.2 Coulomb Gas Perspective -- 7.3 Generalised Partition Function and Probabilities -- 7.4 Skew-Orthogonal Polynomials -- 7.5 Correlation Functions for the Real Eigenvalues -- 7.6 Correlation Functions for Complex Eigenvalues -- 7.7 Fluctuation Formulas for Real Eigenvalues -- 7.8 Relationship to Diffusion Processes and Gap Probabilities -- 7.9 Elliptic GinOE -- 7.10 An Application of Elliptic GinOE to Equilibria Counting.
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8 Analogues of GinUE Statistical Properties for GinOE -- 8.1 Bulk and Edge Correlations -- 8.2 Global Density and Fluctuations -- 8.3 Sum Rules -- 8.4 Singular Values -- 8.5 Real GinOE Eigenvector Statistics -- 9 Further Extensions to GinOE -- 9.1 Common Structures -- 9.2 Induced GinOE -- 9.3 Spherical GinOE -- 9.4 Truncations of Haar Real Orthogonal Matrices -- 9.5 Products of GinOE -- 10 Statistical Properties of GinSE and Elliptic GinSE -- 10.1 Eigenvalue PDF -- 10.2 Coulomb Gas Perspective -- 10.3 Skew-Orthogonal Polynomials -- 10.4 Correlation Functions and Sum Rules -- 10.5 Elliptic GinSE -- 10.6 Partition Functions and Gap Probabilities -- 10.7 GinSE Singular Values -- 10.8 GinSE Eigenvectors -- 11 Further Extensions to GinSE -- 11.1 Common Structures -- 11.2 Induced GinSE -- 11.3 Spherical Induced GinSE -- 11.4 Truncations of Haar Unitary Symplectic Matrices -- 11.5 Products of GinSE -- 11.6 A Summary of GinSE Analogues with GinUE and GinOE -- Appendix References.
Additional Edition:
Print version: Byun, Sung-Soo Progress on the Study of the Ginibre Ensembles Singapore : Springer,c2024 ISBN 9789819751723
Language:
English
Keywords:
Electronic books.
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