Introduction to random matrices : theory and practice /: theory and practice. ([2018])

• Record Type: Book
• Further Information: Note: Giacomo Livan, Marcel Novaes, Pierpaolo Vivo.
• Authors: Livan, Giacomo; Novaes, Marcel; Vivo, Pierpaolo
• Contents: Intro; Preface; Contents; 1 Getting Started; 1.1 One-Pager on Random Variables; 2 Value the Eigenvalue; 2.1 Appetizer: Wigner's Surmise; 2.2 Eigenvalues as Correlated Random Variables; 2.3 Compare with the Spacings Between i.i.d.'s; 2.4 Jpdf of Eigenvalues of Gaussian Matrices; References; 3 Classified Material; 3.1 Count on Dirac; 3.2 Layman's Classification; 3.3 To Know More ... ; References; 4 The Fluid Semicircle; 4.1 Coulomb Gas; 4.2 Do It Yourself (Before Lunch); References; 5 Saddle-Point-of-View; 5.1 Saddle-Point. What's the Point?; 5.2 Disintegrate the Integral Equation. 5.3 Better Weak Than Nothing5.4 Smart Tricks; 5.5 The Final Touch; 5.6 Epilogue; 5.7 To Know More ... ; References; 6 Time for a Change; 6.1 Intermezzo: A Simpler Change of Variables; 6.2 ... that Is the Question; 6.3 Keep Your Volume Under Control; 6.4 For Doubting Thomases ... ; 6.5 Jpdf of Eigenvalues and Eigenvectors; 6.6 Leave the Eigenvalues Alone; 6.7 For Invariant Models ... ; 6.8 The Proof; References; 7 Meet Vandermonde; 7.1 The Vandermonde Determinant; 7.2 Do It Yourself; References; 8 Resolve(nt) the Semicircle; 8.1 A Bit of Theory; 8.2 Averaging; 8.3 Do It Yourself. 8.4 Localize the Resolvent8.5 To Know More ... ; References; 9 One Pager on Eigenvectors; References; 10 Finite N; 10.1 β=2 is Easier; 10.2 Integrating Inwards; 10.3 Do It Yourself; 10.4 Recovering the Semicircle; References; 11 Meet Andréief; 11.1 Some Integrals Involving Determinants; 11.2 Do It Yourself; 11.3 To Know More ... ; References; 12 Finite N Is Not Finished; 12.1 β=1; 12.2 β=4; References; 13 Classical Ensembles: Wishart-Laguerre; 13.1 Wishart-Laguerre Ensemble; 13.2 Jpdf of Entries: Matrix Deltas ... ; 13.3 ... and Matrix Integrals; 13.4 To Know More ... ; References. 14 Meet MarÄ#x8D;enko and Pastur14.1 The MarÄ#x8D;enko-Pastur Density; 14.2 Do It Yourself: The Resolvent Method; 14.3 Correlations in the Real World and a Quick Example: Financial Correlations; References; 15 Replicas ... ; 15.1 Meet Edwards and Jones; 15.2 The Proof; 15.3 Averaging the Logarithm; 15.4 Quenched versus Annealed; References; 16 Replicas for GOE; 16.1 Wigner's Semicircle for GOE: Annealed Calculation; 16.2 Wigner's Semicircle: Quenched Calculation; 16.2.1 Critical Points; 16.2.2 One Step Back: Summarize and Continue; References; 17 Born to Be Free. 17.1 Things About Probability You Probably Already Know17.2 Freeness; 17.3 Free Addition; 17.4 Do It Yourself; References.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 512.9/434; Physics; Random matrices; MATHEMATICS -- Algebra -- Intermediate; Random matrices; Mathematics -- Probability & Statistics -- General; Science -- Mathematical Physics; Science -- Physics; Probability & statistics; Mathematical physics; Statistical physics; Mathematical physics; Distribution (Probability theory); Statistical physics; Electronic books
• Languages: English
• ISBNs: 9783319708850; 3319708856; 9783319708836
• Related ISBNs: 9783319708836; 331970883X
• Notes: Note: Includes bibliographical references.; Note: Vendor-supplied metadata.
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