Combinatorics and random matrix theory:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2016]
|
| Schriftenreihe: | Graduate studies in mathematics
172 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xi, 461 Seiten Illustrationen |
| ISBN: | 9780821848418 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | Titel: Combinatorics and random matrix theory
Autor: Baik, Jinho
Jahr: 2016
Contents Preface xi Chapter 1. Introduction 1 §1.1. Ulam’s Problem: Random Permutations 2 §1.2. Random Tilings of the Aztec Diamond 12 §1.3. General Remarks 14 Chapter 2. Poissonization and De-Poissonization 19 §2.1. Hammersley’s Poissonization of Ulam’s Problem 19 §2.2. De-Poissonization Lemmas 21 Chapter 3. Permutations and Young Tableaux 27 §3.1. The Robinson-Schensted Correspondence 28 §3.2. The Number of Standard Young Tableaux 49 §3.3. Applications and Equivalent Models 63 Chapter 4. Bounds on the Expected Value of £jy 77 §4.1. Lower Bound 77 §4.2. Existence of c 78 §4.3. Young Diagrams in a Markov Chain and an Optimal Upper Bound 82 §4.4. Asymptotics of the Conjugacy Classes of the Symmetric Group 87 vii
Contents viii Chapter 5. Orthogonal Polynomials, Riemann-Hilbert Problems, and Toeplitz Matrices 95 :5.1. Orthogonal Polynomials on the Real Line (OPRL) 95 5.2. Some Classical Orthogonal Polynomials 99 ¡5.3. The Riemann-Hilbert Problem (RHP) for Orthogonal Polynomials 100 §5.4. Orthogonal Polynomials on the Unit Circle (OPUC) and Toeplitz Matrices 106 §5.5. RHP: Precise Description 111 §5.6. Integrable Operators 118 §5.7. The Strong Szego Limit Theorem 121 §5.8. Inverses of Large Toeplitz Matrices 130 Chapter 6. Random Matrix Theory 139 §6.1. Unitary Ensembles and the Eigenvalue Density Function 139 §6.2. Andréief’s Formula and the Computation of Basic Statisitcs 142 §6.3. Gap Probabilities and Correlation Functions 146 §6.4. Scaling Limits and Universality 152 §6.5. The Tracy-Widom Distribution Function 157 Chapter 7. Toeplitz Determinant Formula 165 §7.1. First Proof 167 §7.2. Second Proof 169 §7.3. Recurrence Formulae and Differential Equations 170 §7.4. Heuristic Argument for Convergence of the Scaled Distribution for L(t) to the Tracy-Widom Distribution 184 Chapter 8. Fredholm Determinant Formula 187 §8.1. First Proof: Borodin-Okounkov-Geronimo-Case Identity 190 §8.2. Second Proof 200 Chapter 9. Asymptotic Results 207 §9.1. Exponential Upper Tail Estimate 208 §9.2. Exponential Lower Tail Estimate 214 §9.3. Convergence of L(t)/t and £n/VN 224 §9.4. Central Limit Theorem 226 §9.5. Uniform Tail Estimates and Convergence of Moments 239 §9.6. Transversal Fluctuations 240
Contents IX Chapter 10. Schur Measure and Directed Last Passage Percolation 253 §10.1. Schur Functions 253 §10.2. RSK and Directed Last Passage Percolation 273 §10.3. Special Cases of Directed Last Passage Percolation 280 §10.4. Gessel’s Formula for Schur Measure 290 §10.5. Fredholm Determinant Formula 294 §10.6. Asymptotics of Directed Last Passage Percolation 298 §10.7. Equivalent Models 301 Chapter 11. Determinantal Point Processes 305 Chapter 12. Tiling of the Aztec Diamond 317 §12.1. Nonintersecting Lattice Paths 318 §12.2. Density Function 334 §12.3. Asymptotics 347 Chapter 13. The Dyson Process and the Brownian Dyson Process 377 §13.1. Dyson Process 379 §13.2. Brownian Dyson Process 380 §13.3. Derivation of the Dyson Process and the Brownian Dyson Process 381 §13.4. Noncolliding Property of the Eigenvalues of Matrix Brownian Motion 389 §13.5. Noncolliding Property of the Eigenvalues of the Matrix Ornstein-Uhlenbeck Process 395 §13.6. Nonintersecting Processes 402 Appendix A. Theory of Trace Class Operators and Fredholm Determinants 421 Appendix B. Steepest-descent Method for the Asymptotic Evaluation of Integrals in the Complex Plane 431 Appendix C. Basic Results of Stochastic Calculus 437 Bibliography 445 Index 459
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| building | Verbundindex |
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| classification_tum | MAT 155f |
| ctrlnum | (OCoLC)955203893 (DE-599)BSZ475385438 |
| dewey-full | 511.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.6 |
| dewey-search | 511.6 |
| dewey-sort | 3511.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-10T07:32:56Z |
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| isbn | 9780821848418 |
| language | English |
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| publishDate | 2016 |
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| publisher | American Mathematical Society |
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| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Baik, Jinho 1973- Verfasser (DE-588)133629538 aut Combinatorics and random matrix theory Jinho Baik, Percy Deift, Toufic Suidan Providence, Rhode Island American Mathematical Society [2016] © 2016 xi, 461 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 172 Kombinatorik (DE-588)4031824-2 gnd rswk-swf Stochastische Matrix (DE-588)4057624-3 gnd rswk-swf Kombinatorik (DE-588)4031824-2 s Stochastische Matrix (DE-588)4057624-3 s DE-604 Deift, Percy 1945- Verfasser (DE-588)140992995 aut Suidan, Toufic Mubadda 1975- Verfasser (DE-588)1111816751 aut Graduate studies in mathematics 172 (DE-604)BV009739289 172 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029115169&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baik, Jinho 1973- Deift, Percy 1945- Suidan, Toufic Mubadda 1975- Combinatorics and random matrix theory Graduate studies in mathematics Kombinatorik (DE-588)4031824-2 gnd Stochastische Matrix (DE-588)4057624-3 gnd |
| subject_GND | (DE-588)4031824-2 (DE-588)4057624-3 |
| title | Combinatorics and random matrix theory |
| title_auth | Combinatorics and random matrix theory |
| title_exact_search | Combinatorics and random matrix theory |
| title_full | Combinatorics and random matrix theory Jinho Baik, Percy Deift, Toufic Suidan |
| title_fullStr | Combinatorics and random matrix theory Jinho Baik, Percy Deift, Toufic Suidan |
| title_full_unstemmed | Combinatorics and random matrix theory Jinho Baik, Percy Deift, Toufic Suidan |
| title_short | Combinatorics and random matrix theory |
| title_sort | combinatorics and random matrix theory |
| topic | Kombinatorik (DE-588)4031824-2 gnd Stochastische Matrix (DE-588)4057624-3 gnd |
| topic_facet | Kombinatorik Stochastische Matrix |
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