Quantum probability and spectral analysis of graphs:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2007
|
| Series: | Theoretical and mathematical physics
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XVIII, 371 S. graph. Darst. |
| ISBN: | 9783540488620 3540488626 |
Staff View
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| 100 | 1 | |a Hora, Akihito |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Quantum probability and spectral analysis of graphs |c Akihito Hora ; Nobuaki Obata |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2007 | |
| 300 | |a XVIII, 371 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Theoretical and mathematical physics | |
| 650 | 4 | |a Analyse spectrale | |
| 650 | 7 | |a Grafentheorie |2 gtt | |
| 650 | 4 | |a Graphes, Théorie des | |
| 650 | 7 | |a Kwantummechanica |2 gtt | |
| 650 | 4 | |a Probabilités | |
| 650 | 7 | |a Spectrumanalyse |2 gtt | |
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| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Graph theory | |
| 650 | 4 | |a Probabilities | |
| 650 | 4 | |a Quantum theory | |
| 650 | 4 | |a Spectrum analysis | |
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Record in the Search Index
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| adam_text |
Contents
1 Quantum Probability and Orthogonal Polynomials 1
1.1 Algebraic Probability Spaces 1
1.2 Representations 6
1.3 Interacting Fock Probability Spaces 11
1.4 The Moment Problem and Orthogonal Polynomials 14
1.5 Quantum Decomposition 23
1.6 The Accardi Bozejko Formula 28
1.7 Fermion, Free and Boson Fock Spaces 36
1.8 Theory of Finite Jacobi Matrices 42
1.9 Stieltjes Transform and Continued Fractions 51
Exercises 59
Notes 62
2 Adjacency Matrices 65
2.1 Notions in Graph Theory 65
2.2 Adjacency Matrices and Adjacency Algebras 67
2.3 Vacuum and Deformed Vacuum States 70
2.4 Quantum Decomposition of an Adjacency Matrix 75
Exercises 80
Notes 83
3 Distance Regular Graphs 85
3.1 Definition and Some Properties 85
3.2 Spectral Distributions in the Vacuum States 88
3.3 Finite Distance Regular Graphs 91
3.4 Asymptotic Spectral Distributions 94
3.5 Coherent States in General 100
Exercises 101
Notes 103
XVI Contents
4 Homogeneous Trees 105
4.1 Kesten Distribution 105
4.2 Asymptotic Spectral Distributions in the Vacuum State (Free
CLT) 109
4.3 The Haagerup State 110
4.4 Free Poisson Distribution 118
4.5 Spidernets and Free Meixner Law 120
4.6 Markov Product of Positive Definite Kernels 125
Exercises 128
Notes 129
5 Hamming Graphs 131
5.1 Definition and Some Properties 131
5.2 Asymptotic Spectral Distributions
in the Vacuum State 134
5.3 Poisson Distribution 136
5.4 Asymptotic Spectral Distributions
in the Deformed Vacuum States 140
Exercises 145
Notes 146
6 Johnson Graphs 147
6.1 Definition and Some Properties 147
6.2 Asymptotic Spectral Distributions
in the Vacuum State 152
6.3 Exponential Distribution and Laguerre Polynomials 154
6.4 Geometric Distribution and Meixner Polynomials 156
6.5 Asymptotic Spectral Distributions
in the Deformed Vacuum States 159
6.6 Odd Graphs 166
Exercises 171
Notes 173
7 Regular Graphs 175
7.1 Integer Lattices 175
7.2 Growing Regular Graphs 177
7.3 Quantum Central Limit Theorems 182
7.4 Deformed Vacuum States 189
7.5 Examples and Remarks 193
Exercises 201
Notes 202
Contents XVII
8 Comb Graphs and Star Graphs 205
8.1 Notions of Independence 205
8.2 Singleton Condition and Central Limit Theorems 210
8.3 Integer Lattices and Homogeneous Trees: Revisited 216
8.4 Monotone Trees and Monotone Central Limit Theorem 219
8.5 Comb Product 229
8.6 Comb Lattices 233
8.7 Star Product 238
Exercises 244
Notes 245
9 The Symmetric Group and Young Diagrams 249
9.1 Young Diagrams 249
9.2 Irreducible Representations of the Symmetric Group 253
9.3 The Jucys Murphy Element 257
9.4 Analytic Description of a Young Diagram 259
9.5 A Basic Trace Formula 263
9.6 Plancherel Measures 267
Exercises 269
Notes 270
10 The Limit Shape of Young Diagrams 271
10.1 Continuous Diagrams 271
10.2 The Limit Shape of Young Diagrams 275
10.3 The Modified Young Graph 277
10.4 Moments of the Jucys Murphy Element 280
10.5 The Limit Shape as a Weak Law of Large Numbers 283
10.6 More on Moments of the Jucys Murphy Element 285
10.7 The Limit Shape as a Strong Law of Large Numbers 293
Exercises 295
Notes 295
11 Central Limit Theorem for the Plancherel Measures of
the Symmetric Groups 297
11.1 Kcrov's Central Limit Theorem and Fluctuation of Young
Diagrams 297
11.2 Use of Quantum Decomposition 299
11.3 Quantum Central Limit Theorem for Adjacency Matrices 301
11.4 Proof of QCLT for Adjacency Matrices 306
11.5 Polynomial Functions on Young Diagrams 310
11.6 Kerov's Polynomials 313
11.7 Other Extensions of Kerov's Central Limit Theorem 314
11.8 More Refinements of Fluctuation 317
Exercises 319
Notes 319
XVIII Contents
12 Deformation of Kerov's Central Limit Theorem 321
12.1 Jack Symmetric Functions 321
12.2 Jack Graphs 325
12.3 Deformed Young Diagrams 327
12.4 Jack Measures 330
12.5 Deformed Adjacency Matrices 334
12.6 Central Limit Theorem for the Jack Measures 340
12.7 The Metropolis Algorithm and Hanlon's Theorem 345
Exercises 349
Notes 349
References 351
Index 363 |
| adam_txt |
Contents
1 Quantum Probability and Orthogonal Polynomials 1
1.1 Algebraic Probability Spaces 1
1.2 Representations 6
1.3 Interacting Fock Probability Spaces 11
1.4 The Moment Problem and Orthogonal Polynomials 14
1.5 Quantum Decomposition 23
1.6 The Accardi Bozejko Formula 28
1.7 Fermion, Free and Boson Fock Spaces 36
1.8 Theory of Finite Jacobi Matrices 42
1.9 Stieltjes Transform and Continued Fractions 51
Exercises 59
Notes 62
2 Adjacency Matrices 65
2.1 Notions in Graph Theory 65
2.2 Adjacency Matrices and Adjacency Algebras 67
2.3 Vacuum and Deformed Vacuum States 70
2.4 Quantum Decomposition of an Adjacency Matrix 75
Exercises 80
Notes 83
3 Distance Regular Graphs 85
3.1 Definition and Some Properties 85
3.2 Spectral Distributions in the Vacuum States 88
3.3 Finite Distance Regular Graphs 91
3.4 Asymptotic Spectral Distributions 94
3.5 Coherent States in General 100
Exercises 101
Notes 103
XVI Contents
4 Homogeneous Trees 105
4.1 Kesten Distribution 105
4.2 Asymptotic Spectral Distributions in the Vacuum State (Free
CLT) 109
4.3 The Haagerup State 110
4.4 Free Poisson Distribution 118
4.5 Spidernets and Free Meixner Law 120
4.6 Markov Product of Positive Definite Kernels 125
Exercises 128
Notes 129
5 Hamming Graphs 131
5.1 Definition and Some Properties 131
5.2 Asymptotic Spectral Distributions
in the Vacuum State 134
5.3 Poisson Distribution 136
5.4 Asymptotic Spectral Distributions
in the Deformed Vacuum States 140
Exercises 145
Notes 146
6 Johnson Graphs 147
6.1 Definition and Some Properties 147
6.2 Asymptotic Spectral Distributions
in the Vacuum State 152
6.3 Exponential Distribution and Laguerre Polynomials 154
6.4 Geometric Distribution and Meixner Polynomials 156
6.5 Asymptotic Spectral Distributions
in the Deformed Vacuum States 159
6.6 Odd Graphs 166
Exercises 171
Notes 173
7 Regular Graphs 175
7.1 Integer Lattices 175
7.2 Growing Regular Graphs 177
7.3 Quantum Central Limit Theorems 182
7.4 Deformed Vacuum States 189
7.5 Examples and Remarks 193
Exercises 201
Notes 202
Contents XVII
8 Comb Graphs and Star Graphs 205
8.1 Notions of Independence 205
8.2 Singleton Condition and Central Limit Theorems 210
8.3 Integer Lattices and Homogeneous Trees: Revisited 216
8.4 Monotone Trees and Monotone Central Limit Theorem 219
8.5 Comb Product 229
8.6 Comb Lattices 233
8.7 Star Product 238
Exercises 244
Notes 245
9 The Symmetric Group and Young Diagrams 249
9.1 Young Diagrams 249
9.2 Irreducible Representations of the Symmetric Group 253
9.3 The Jucys Murphy Element 257
9.4 Analytic Description of a Young Diagram 259
9.5 A Basic Trace Formula 263
9.6 Plancherel Measures 267
Exercises 269
Notes 270
10 The Limit Shape of Young Diagrams 271
10.1 Continuous Diagrams 271
10.2 The Limit Shape of Young Diagrams 275
10.3 The Modified Young Graph 277
10.4 Moments of the Jucys Murphy Element 280
10.5 The Limit Shape as a Weak Law of Large Numbers 283
10.6 More on Moments of the Jucys Murphy Element 285
10.7 The Limit Shape as a Strong Law of Large Numbers 293
Exercises 295
Notes 295
11 Central Limit Theorem for the Plancherel Measures of
the Symmetric Groups 297
11.1 Kcrov's Central Limit Theorem and Fluctuation of Young
Diagrams 297
11.2 Use of Quantum Decomposition 299
11.3 Quantum Central Limit Theorem for Adjacency Matrices 301
11.4 Proof of QCLT for Adjacency Matrices 306
11.5 Polynomial Functions on Young Diagrams 310
11.6 Kerov's Polynomials 313
11.7 Other Extensions of Kerov's Central Limit Theorem 314
11.8 More Refinements of Fluctuation 317
Exercises 319
Notes 319
XVIII Contents
12 Deformation of Kerov's Central Limit Theorem 321
12.1 Jack Symmetric Functions 321
12.2 Jack Graphs 325
12.3 Deformed Young Diagrams 327
12.4 Jack Measures 330
12.5 Deformed Adjacency Matrices 334
12.6 Central Limit Theorem for the Jack Measures 340
12.7 The Metropolis Algorithm and Hanlon's Theorem 345
Exercises 349
Notes 349
References 351
Index 363 |
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| id | DE-604.BV022524714 |
| illustrated | Illustrated |
| index_date | 2024-07-02T18:04:32Z |
| indexdate | 2024-07-20T09:20:37Z |
| institution | BVB |
| isbn | 9783540488620 3540488626 |
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| physical | XVIII, 371 S. graph. Darst. |
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| record_format | marc |
| series2 | Theoretical and mathematical physics |
| spelling | Hora, Akihito Verfasser aut Quantum probability and spectral analysis of graphs Akihito Hora ; Nobuaki Obata Berlin [u.a.] Springer 2007 XVIII, 371 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Theoretical and mathematical physics Analyse spectrale Grafentheorie gtt Graphes, Théorie des Kwantummechanica gtt Probabilités Spectrumanalyse gtt Théorie quantique Waarschijnlijkheidstheorie gtt Quantentheorie Graph theory Probabilities Quantum theory Spectrum analysis Graphentheorie (DE-588)4113782-6 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Spektralanalyse Stochastik (DE-588)4056125-2 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Spektralanalyse Stochastik (DE-588)4056125-2 s Graphentheorie (DE-588)4113782-6 s DE-604 Obata, Nobuaki 1957- Verfasser (DE-588)113940424 aut text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2874138&prov=M&dok_var=1&dok_ext=htm Inhaltstext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015731405&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hora, Akihito Obata, Nobuaki 1957- Quantum probability and spectral analysis of graphs Analyse spectrale Grafentheorie gtt Graphes, Théorie des Kwantummechanica gtt Probabilités Spectrumanalyse gtt Théorie quantique Waarschijnlijkheidstheorie gtt Quantentheorie Graph theory Probabilities Quantum theory Spectrum analysis Graphentheorie (DE-588)4113782-6 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Quantenmechanik (DE-588)4047989-4 gnd Spektralanalyse Stochastik (DE-588)4056125-2 gnd |
| subject_GND | (DE-588)4113782-6 (DE-588)4079013-7 (DE-588)4047989-4 (DE-588)4056125-2 |
| title | Quantum probability and spectral analysis of graphs |
| title_auth | Quantum probability and spectral analysis of graphs |
| title_exact_search | Quantum probability and spectral analysis of graphs |
| title_exact_search_txtP | Quantum probability and spectral analysis of graphs |
| title_full | Quantum probability and spectral analysis of graphs Akihito Hora ; Nobuaki Obata |
| title_fullStr | Quantum probability and spectral analysis of graphs Akihito Hora ; Nobuaki Obata |
| title_full_unstemmed | Quantum probability and spectral analysis of graphs Akihito Hora ; Nobuaki Obata |
| title_short | Quantum probability and spectral analysis of graphs |
| title_sort | quantum probability and spectral analysis of graphs |
| topic | Analyse spectrale Grafentheorie gtt Graphes, Théorie des Kwantummechanica gtt Probabilités Spectrumanalyse gtt Théorie quantique Waarschijnlijkheidstheorie gtt Quantentheorie Graph theory Probabilities Quantum theory Spectrum analysis Graphentheorie (DE-588)4113782-6 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Quantenmechanik (DE-588)4047989-4 gnd Spektralanalyse Stochastik (DE-588)4056125-2 gnd |
| topic_facet | Analyse spectrale Grafentheorie Graphes, Théorie des Kwantummechanica Probabilités Spectrumanalyse Théorie quantique Waarschijnlijkheidstheorie Quantentheorie Graph theory Probabilities Quantum theory Spectrum analysis Graphentheorie Wahrscheinlichkeitstheorie Quantenmechanik Spektralanalyse Stochastik |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2874138&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015731405&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT horaakihito quantumprobabilityandspectralanalysisofgraphs AT obatanobuaki quantumprobabilityandspectralanalysisofgraphs |