Eigenvalue distribution of large random matrices:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, R.I.
American Mathematical Soc.
2011
|
| Schriftenreihe: | Mathematical surveys and monographs
171 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XIV, 632 S. |
| ISBN: | 9780821852859 082185285X |
Internformat
MARC
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| 035 | |a (DE-599)BVBBV039742765 | ||
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| 100 | 1 | |a Pastur, Leonid A. |d 1937- |e Verfasser |0 (DE-588)1017161844 |4 aut | |
| 245 | 1 | 0 | |a Eigenvalue distribution of large random matrices |c Leonid Pastur ; Mariya Shcherbina |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Soc. |c 2011 | |
| 300 | |a XIV, 632 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical surveys and monographs |v 171 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Distribution (Probability theory) | |
| 650 | 4 | |a Random matrices | |
| 650 | 7 | |a Probability theory and stochastic processes / Limit theorems / Central limit and other weak theorems |2 msc | |
| 650 | 7 | |a Probability theory and stochastic processes / Probability theory on algebraic and topological structures / Random matrices (probabilistic aspects; for algebraic aspects see 15B52) |2 msc | |
| 650 | 7 | |a Linear and multilinear algebra; matrix theory / Special matrices / Random matrices |2 msc | |
| 650 | 7 | |a Linear and multilinear algebra; matrix theory / Special matrices / Hermitian, skew-Hermitian, and related matrices |2 msc | |
| 650 | 0 | 7 | |a Wahrscheinlichkeitsverteilung |0 (DE-588)4121894-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stochastische Matrix |0 (DE-588)4057624-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Wahrscheinlichkeitsverteilung |0 (DE-588)4121894-2 |D s |
| 689 | 0 | 1 | |a Stochastische Matrix |0 (DE-588)4057624-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Shcherbina, Mariya |d 1958- |e Sonstige |0 (DE-588)1017138532 |4 oth | |
| 830 | 0 | |a Mathematical surveys and monographs |v 171 |w (DE-604)BV000018014 |9 171 | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024590394&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-024590394 | ||
Datensatz im Suchindex
| _version_ | 1804148630773301248 |
|---|---|
| adam_text | Contents
Preface
їх
Chapter
1.
Introduction
1
1.1.
Objectives and Problems
1
1.2.
Example
13
1.3.
Comments and Problems
21
Part
1.
Classical Ensembles
33
Chapter
2.
Gaussian Ensembles: Semicircle Law
35
2.1.
Technical Means
35
2.2.
Deformed Semicircle Law
43
2.3.
The Case of Random tf <°)
54
2.4.
Problems
59
Chapter
3.
Gaussian Ensembles: Central Limit Theorem for Linear
Eigenvalue Statistics
69
3.1.
Covariance for Traces of the Resolvent
69
3.2.
Central Limit Theorem for Linear Eigenvalue Statistics of
Differentiable Test Functions
74
3.3.
Central Limit Theorem for
(ψ{Μ))^
90
3.4.
Problems
94
Chapter
4.
Gaussian Ensembles: Joint Eigenvalue Distribution and Related
Results
101
4.1.
Joint Eigenvalue Probability Density
101
4.2.
Orthogonal Polynomial Techniques
107
4.3.
Simplest Applications
113
4.4.
Comments and Problems
118
Chapter
5.
Gaussian Unitary Ensemble
129
5.1.
Hermite Polynomials
129
5.2.
Bulk of the Spectrum
131
5.3.
Edges of the Spectrum
147
5.4.
Problems
152
Chapter
6.
Gaussian Orthogonal Ensemble
159
6.1.
Correlation and Cluster Functions
159
6.2.
Bulk of the Spectrum
166
6.3.
Edges of the Spectrum
171
6.4.
Problems
175
vi
CONTENTS
Chapter
7.
Wishart
and Laguerre Ensembles
177
7.1.
Generalities
177
7.2.
Normalized Counting Measure of Eigenvalues
182
7.3.
Central Limit Theorem for Linear Eigenvalue Statistics
189
7.4.
Joint Eigenvalue Distribution
192
7.5.
Local Regimes
195
7.6.
Comments and Problems
203
Chapter
8.
Classical Compact Group Ensembles: Global Regime
211
8.1.
Classical Compact Groups as Random Matrix Ensembles
211
8.2.
Limiting Normalized Counting Measure and Central Limit Theorem
for Linear Eigenvalue Statistics of Unitary Matrices
218
8.3.
Moments of Traces of Matrices of Classical Compact Groups
222
8.4.
More Central Limit Theorems for Linear Eigenvalue Statistics of
Matrices of Classical Groups
234
8.5.
Problems
244
Chapter
9.
Classical Compact Group Ensembles: Further Results
249
9.1.
Joint Eigenvalue Distribution and Related Results
249
9.2.
Circular Ensembles
264
9.3.
Problems
273
Chapter
10.
Law of Addition of Random Matrices
275
10.1.
Normalized Counting Measure of Eigenvalues
276
10.2.
Fluctuations of the Traces of Resolvents
290
10.3.
The Case of Many Summands
304
10.4.
Problems
306
Part
2.
Matrix Models
315
Chapter
11.
Matrix Models: Global Regime
317
11.1.
Convergence of the Normalized Counting Measure of Eigenvalues
317
11.2.
Properties of the Limiting Measure
338
11.3.
Fluctuations of the Normalized Counting Measure of Eigenvalues
352
11.4.
Comments and Problems
359
Chapter
12.
Bulk Universality for Hermitian Matrix Models
369
12.1.
Basic Results
369
12.2.
Proof of Basic Results
370
12.3.
Problems
383
Chapter
13.
Universality for Special Points of Hermitian Matrix Models
385
13.1.
Generic Soft Edges
386
13.2.
Internal Points
408
13.3.
Some Properties of Jacobi Matrices
431
13.4.
Problems
435
Chapter
14.
Jacobi Matrices and Limiting Laws for Linear Eigenvalue
Statistics
437
14.1.
Asymptotics of Orthogonal Polynomials and Quasiperiodic Jacobi
Matrices
437
CONTENTS
vii
14.2.
Fluctuations
of Linear Eigenvalue Statistics
451
14.3.
Intermediate and Local Regimes
464
14.4.
Problems
466
Chapter
15.
Universality for Real Symmetric Matrix Models
469
15.1.
Generalities
469
15.2.
Invertibility of M^n)
472
15.3.
Universality for Real Symmetric Matrix Models
478
15.4.
Problems
483
Chapter
16.
Unitary Matrix Models
485
16.1.
Global Regime
485
16.2.
Bulk Universality for Unitary Matrix Models
494
16.3.
Problems
498
Part
3.
Ensembles with Independent and Weakly Dependent
Entries
499
Chapter
17.
Matrices with Gaussian Correlated Entries
501
17.1.
Definition and Finite-
η
Results
501
17.2.
Limiting Equations
504
17.3.
Parametric Limits for Certain Ergodic Operators
509
17.4.
Problems
522
Chapter
18.
Wigner Ensembles
525
18.1.
Generalities
525
18.2.
Martingale Bounds for Moments of Spectral Characteristics
531
18.3.
Deformed Semicircle Law
535
18.4.
Central Limit Theorem for Linear Eigenvalue Statistics
539
18.5.
Further Asymptotic Results on Linear Eigenvalue Statistics
556
18.6.
Limits of Extreme Eigenvalues
559
18.7.
Other Results
565
18.8.
Problems
580
Chapter
19.
Sample Covariance and Related Matrices
583
19.1.
Limiting Normalized Counting Measure of Eigenvalues
583
19.2.
Central Limit Theorem for Linear Eigenvalue Statistics
597
19.3.
Other Results
607
Bibliography
611
Index
631
|
| any_adam_object | 1 |
| author | Pastur, Leonid A. 1937- |
| author_GND | (DE-588)1017161844 (DE-588)1017138532 |
| author_facet | Pastur, Leonid A. 1937- |
| author_role | aut |
| author_sort | Pastur, Leonid A. 1937- |
| author_variant | l a p la lap |
| building | Verbundindex |
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| dewey-full | 519.2/4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/4 |
| dewey-search | 519.2/4 |
| dewey-sort | 3519.2 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV039742765 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:10:12Z |
| institution | BVB |
| isbn | 9780821852859 082185285X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024590394 |
| oclc_num | 692084739 |
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| owner | DE-188 DE-19 DE-BY-UBM DE-703 |
| owner_facet | DE-188 DE-19 DE-BY-UBM DE-703 |
| physical | XIV, 632 S. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | American Mathematical Soc. |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Pastur, Leonid A. 1937- Verfasser (DE-588)1017161844 aut Eigenvalue distribution of large random matrices Leonid Pastur ; Mariya Shcherbina Providence, R.I. American Mathematical Soc. 2011 XIV, 632 S. txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs 171 Includes bibliographical references and index Distribution (Probability theory) Random matrices Probability theory and stochastic processes / Limit theorems / Central limit and other weak theorems msc Probability theory and stochastic processes / Probability theory on algebraic and topological structures / Random matrices (probabilistic aspects; for algebraic aspects see 15B52) msc Linear and multilinear algebra; matrix theory / Special matrices / Random matrices msc Linear and multilinear algebra; matrix theory / Special matrices / Hermitian, skew-Hermitian, and related matrices msc Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd rswk-swf Stochastische Matrix (DE-588)4057624-3 gnd rswk-swf Wahrscheinlichkeitsverteilung (DE-588)4121894-2 s Stochastische Matrix (DE-588)4057624-3 s DE-604 Shcherbina, Mariya 1958- Sonstige (DE-588)1017138532 oth Mathematical surveys and monographs 171 (DE-604)BV000018014 171 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024590394&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pastur, Leonid A. 1937- Eigenvalue distribution of large random matrices Mathematical surveys and monographs Distribution (Probability theory) Random matrices Probability theory and stochastic processes / Limit theorems / Central limit and other weak theorems msc Probability theory and stochastic processes / Probability theory on algebraic and topological structures / Random matrices (probabilistic aspects; for algebraic aspects see 15B52) msc Linear and multilinear algebra; matrix theory / Special matrices / Random matrices msc Linear and multilinear algebra; matrix theory / Special matrices / Hermitian, skew-Hermitian, and related matrices msc Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Stochastische Matrix (DE-588)4057624-3 gnd |
| subject_GND | (DE-588)4121894-2 (DE-588)4057624-3 |
| title | Eigenvalue distribution of large random matrices |
| title_auth | Eigenvalue distribution of large random matrices |
| title_exact_search | Eigenvalue distribution of large random matrices |
| title_full | Eigenvalue distribution of large random matrices Leonid Pastur ; Mariya Shcherbina |
| title_fullStr | Eigenvalue distribution of large random matrices Leonid Pastur ; Mariya Shcherbina |
| title_full_unstemmed | Eigenvalue distribution of large random matrices Leonid Pastur ; Mariya Shcherbina |
| title_short | Eigenvalue distribution of large random matrices |
| title_sort | eigenvalue distribution of large random matrices |
| topic | Distribution (Probability theory) Random matrices Probability theory and stochastic processes / Limit theorems / Central limit and other weak theorems msc Probability theory and stochastic processes / Probability theory on algebraic and topological structures / Random matrices (probabilistic aspects; for algebraic aspects see 15B52) msc Linear and multilinear algebra; matrix theory / Special matrices / Random matrices msc Linear and multilinear algebra; matrix theory / Special matrices / Hermitian, skew-Hermitian, and related matrices msc Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Stochastische Matrix (DE-588)4057624-3 gnd |
| topic_facet | Distribution (Probability theory) Random matrices Probability theory and stochastic processes / Limit theorems / Central limit and other weak theorems Probability theory and stochastic processes / Probability theory on algebraic and topological structures / Random matrices (probabilistic aspects; for algebraic aspects see 15B52) Linear and multilinear algebra; matrix theory / Special matrices / Random matrices Linear and multilinear algebra; matrix theory / Special matrices / Hermitian, skew-Hermitian, and related matrices Wahrscheinlichkeitsverteilung Stochastische Matrix |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024590394&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
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