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Introduction to Random Matrices : Theory and Practice.

By: Livan, Giacomo.
Contributor(s): Novaes, Marcel | Vivo, Pierpaolo.
Material type: TextTextSeries: eBooks on Demand.SpringerBriefs in Mathematical Physics Ser: Publisher: Cham : Springer, 2018Copyright date: ©2018Description: 1 online resource (122 pages).Content type: text Media type: computer Carrier type: online resourceISBN: 9783319708850.Subject(s): Random matricesGenre/Form: Electronic books.Additional physical formats: Print version:: Introduction to Random Matrices : Theory and PracticeDDC classification: 512.9434 LOC classification: QC5.53QA273.A1-274.9Online resources: Click here to view this ebook.
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 Nothing -- 5.4 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 Resolvent -- 8.5 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 Marčenko and Pastur -- 14.1 The Marčenko-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 Know -- 17.2 Freeness -- 17.3 Free Addition -- 17.4 Do It Yourself -- References.
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Item type Current location Call number URL Status Date due Barcode
Electronic Book UT Tyler Online
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QC5.53QA273.A1-274.9 (Browse shelf) https://ebookcentral.proquest.com/lib/uttyler/detail.action?docID=5224852 Available EBC5224852

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 Nothing -- 5.4 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 Resolvent -- 8.5 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 Marčenko and Pastur -- 14.1 The Marčenko-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 Know -- 17.2 Freeness -- 17.3 Free Addition -- 17.4 Do It Yourself -- References.

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