Introduction to random matrices: theory and practice
Gespeichert in:
| Hauptverfasser: | , , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham
Springer
[2018]
|
| Schriftenreihe: | SpringerBriefs in Mathematical Physics
volume 26 |
| Schlagworte: | |
| Online-Zugang: | UBM01 UBT01 UER01 Inhaltsverzeichnis |
| Beschreibung: | IX, 124 Seiten Illustrationen |
| ISBN: | 9783319708836 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804182096361553920 |
|---|---|
| adam_text | Contents 1 Getting Started................................................................................................ 1.1 2 One-Pager on Random Variables.................................................... Value the Eigenvalue .................................................................................... 2.1 Appetizer: Wigner’s Surmise........................................................... 2.2 Eigenvalues as Correlated RandomVariables................................ 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 Nothing.............................................................. 5.4 Smart Tricks........................................................................................ 5.5 The Final Touch................................................................................. 5.6 Epilogue............................................................................................... 5.7 To Know More................................................................................... References..................................................................................................... 1 3 7 7 9 9 11 13 15 15 18 21 21 23 23 25 31 33 33 35 35 37 38 39 42 43 vii
viii Contents 6 Time for a Change..................................................................................... 6.1 Intermezzo: A SimplerChange 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..................................................................................................... 45 45 46 46 47 48 49 49 50 51 7 Meet Vandermonde..................................................................................... 7.1 The Vandermonde Determinant...................................................... 7.2 Do It Yourself.................................................................................. References..................................................................................................... 53 53 54 56 8 Resolve(nt) the Semicircle.......................................................................... 8.1 A Bit of
Theory................................................................................ 8.2 Averaging......................................................................................... 8.3 Do It Yourself.................................................................................. 8.4 Localize the Resolvent.................................................................... 8.5 To Know More................................................................................... References..................................................................................................... 57 57 58 60 62 63 63 9 One Pager on Eigenvectors....................................................................... References..................................................................................................... 65 66 10 Finite N.......................................................................................................... 10.1 ß = 2 is Easier................................................................................... 10.2 Integrating Inwards........................................................................... 10.3 Do It Yourself.................................................................................. 10.4 Recovering the Semicircle............................................................... References..................................................................................................... 67 67 70 72 73 74 11 Meet Andréief............................................................................................... 11.1
Some Integrals Involving Determinants........................................ 11.2 Do It Yourself................................................................................... 11.3 To Know More................................................................................... References..................................................................................................... 75 75 77 78 79 12 Finite N Is Not Finished............................................................................ 12.1 0=1................................................................................................... 12.2 ß = 4................................................................................................... References..................................................................................................... 81 81 86 87 13 Classical Ensembles: Wishart-Laguerre................................................ 13.1 Wishart-Laguerre Ensemble............................................................. 89 89
Contents ix 13.2 Jpdf of Entries: Matrix Deltas.......................................................... 13.3 ...and Matrix Integrals...................................................................... 13.4 To Know More................................................................................... References..................................................................................................... 91 93 94 95 Marčenko and Pastur...................................................................... The Marčenko-Pastur Density....................................................... Do It Yourself: The Resolvent Method....................................... Correlations in the Real World and a Quick Example: Financial Correlations............................................................ 101 References..................................................................................................... 97 97 98 103 15 Replicas......................................................................................................... 15.1 Meet Edwards and Jones................................................................. 15.2 The Proof........................................................................................... 15.3 Averaging the Logarithm................................................................. 15.4 Quenched versus Annealed............................................................ References..................................................................................................... 105 105 106 107 107 108 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..................................................................................................... 109 109 112 114 116 117 17 Born to Be Free........................................................................................ 17.1 Things About Probability You Probably AlreadyKnow............. 17.2 Freeness.............................................................................................. 17.3 Free Addition.................................................................................... 17.4 Do It Yourself.................................................................................. References..................................................................................................... 119 119 120 121 122 124 14 Meet 14.1 14.2 14.3
|
| adam_txt |
Contents 1 Getting Started. 1.1 2 One-Pager on Random Variables. Value the Eigenvalue . 2.1 Appetizer: Wigner’s Surmise. 2.2 Eigenvalues as Correlated RandomVariables. 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 Nothing. 5.4 Smart Tricks. 5.5 The Final Touch. 5.6 Epilogue. 5.7 To Know More. References. 1 3 7 7 9 9 11 13 15 15 18 21 21 23 23 25 31 33 33 35 35 37 38 39 42 43 vii
viii Contents 6 Time for a Change. 6.1 Intermezzo: A SimplerChange 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. 45 45 46 46 47 48 49 49 50 51 7 Meet Vandermonde. 7.1 The Vandermonde Determinant. 7.2 Do It Yourself. References. 53 53 54 56 8 Resolve(nt) the Semicircle. 8.1 A Bit of
Theory. 8.2 Averaging. 8.3 Do It Yourself. 8.4 Localize the Resolvent. 8.5 To Know More. References. 57 57 58 60 62 63 63 9 One Pager on Eigenvectors. References. 65 66 10 Finite N. 10.1 ß = 2 is Easier. 10.2 Integrating Inwards. 10.3 Do It Yourself. 10.4 Recovering the Semicircle. References. 67 67 70 72 73 74 11 Meet Andréief. 11.1
Some Integrals Involving Determinants. 11.2 Do It Yourself. 11.3 To Know More. References. 75 75 77 78 79 12 Finite N Is Not Finished. 12.1 0=1. 12.2 ß = 4. References. 81 81 86 87 13 Classical Ensembles: Wishart-Laguerre. 13.1 Wishart-Laguerre Ensemble. 89 89
Contents ix 13.2 Jpdf of Entries: Matrix Deltas. 13.3 .and Matrix Integrals. 13.4 To Know More. References. 91 93 94 95 Marčenko and Pastur. The Marčenko-Pastur Density. Do It Yourself: The Resolvent Method. Correlations in the Real World and a Quick Example: Financial Correlations. 101 References. 97 97 98 103 15 Replicas. 15.1 Meet Edwards and Jones. 15.2 The Proof. 15.3 Averaging the Logarithm. 15.4 Quenched versus Annealed. References. 105 105 106 107 107 108 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. 109 109 112 114 116 117 17 Born to Be Free. 17.1 Things About Probability You Probably AlreadyKnow. 17.2 Freeness. 17.3 Free Addition. 17.4 Do It Yourself. References. 119 119 120 121 122 124 14 Meet 14.1 14.2 14.3 |
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| spelling | Livan, Giacomo Verfasser (DE-588)1160260656 aut Introduction to random matrices theory and practice Giacomo Livan, Marcel Novaes, Pierpaolo Vivo Cham Springer [2018] IX, 124 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier SpringerBriefs in Mathematical Physics volume 26 Physics System theory Probabilities Mathematical physics Mathematical Methods in Physics Probability Theory and Stochastic Processes Mathematical Physics Statistical Physics and Dynamical Systems Complex Systems Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Stochastische Matrix (DE-588)4057624-3 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Stochastische Matrix (DE-588)4057624-3 s Mathematische Physik (DE-588)4037952-8 s DE-604 Novaes, Marcel Verfasser (DE-588)116026094X aut Vivo, Pierpaolo Verfasser (DE-588)1160260877 aut Erscheint auch als Online-Ausgabe 978-3-319-70885-0 SpringerBriefs in Mathematical Physics volume 26 (DE-604)BV041997379 26 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032490496&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Livan, Giacomo Novaes, Marcel Vivo, Pierpaolo Introduction to random matrices theory and practice SpringerBriefs in Mathematical Physics Physics System theory Probabilities Mathematical physics Mathematical Methods in Physics Probability Theory and Stochastic Processes Mathematical Physics Statistical Physics and Dynamical Systems Complex Systems Mathematische Physik (DE-588)4037952-8 gnd Stochastische Matrix (DE-588)4057624-3 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4057624-3 (DE-588)4123623-3 |
| title | Introduction to random matrices theory and practice |
| title_auth | Introduction to random matrices theory and practice |
| title_exact_search | Introduction to random matrices theory and practice |
| title_exact_search_txtP | Introduction to random matrices theory and practice |
| title_full | Introduction to random matrices theory and practice Giacomo Livan, Marcel Novaes, Pierpaolo Vivo |
| title_fullStr | Introduction to random matrices theory and practice Giacomo Livan, Marcel Novaes, Pierpaolo Vivo |
| title_full_unstemmed | Introduction to random matrices theory and practice Giacomo Livan, Marcel Novaes, Pierpaolo Vivo |
| title_short | Introduction to random matrices |
| title_sort | introduction to random matrices theory and practice |
| title_sub | theory and practice |
| topic | Physics System theory Probabilities Mathematical physics Mathematical Methods in Physics Probability Theory and Stochastic Processes Mathematical Physics Statistical Physics and Dynamical Systems Complex Systems Mathematische Physik (DE-588)4037952-8 gnd Stochastische Matrix (DE-588)4057624-3 gnd |
| topic_facet | Physics System theory Probabilities Mathematical physics Mathematical Methods in Physics Probability Theory and Stochastic Processes Mathematical Physics Statistical Physics and Dynamical Systems Complex Systems Mathematische Physik Stochastische Matrix Lehrbuch |
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