Ebook: Quantum Probability and Spectral Analysis of Graphs
- Genre: Mathematics // Probability
- Tags: Mathematical Methods in Physics, Algebra, Quantum Physics
- Series: Theoretical and Mathematical Physics
- Year: 2007
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
This is the first book to comprehensively cover the quantum probabilistic approach to spectral analysis of graphs. This approach has been developed by the authors and has become an interesting research area in applied mathematics and physics. The book can be used as a concise introduction to quantum probability from an algebraic aspect. Here readers will learn several powerful methods and techniques of wide applicability, which have been recently developed under the name of quantum probability. The exercises at the end of each chapter help to deepen understanding.
Among the topics discussed along the way are: quantum probability and orthogonal polynomials; asymptotic spectral theory (quantum central limit theorems) for adjacency matrices; the method of quantum decomposition; notions of independence and structure of graphs; and asymptotic representation theory of the symmetric groups.
This is the first book to comprehensively cover the quantum probabilistic approach to spectral analysis of graphs. This approach has been developed by the authors and has become an interesting research area in applied mathematics and physics. The book can be used as a concise introduction to quantum probability from an algebraic aspect. Here readers will learn several powerful methods and techniques of wide applicability, which have been recently developed under the name of quantum probability. The exercises at the end of each chapter help to deepen understanding.
Among the topics discussed along the way are: quantum probability and orthogonal polynomials; asymptotic spectral theory (quantum central limit theorems) for adjacency matrices; the method of quantum decomposition; notions of independence and structure of graphs; and asymptotic representation theory of the symmetric groups.
This is the first book to comprehensively cover the quantum probabilistic approach to spectral analysis of graphs. This approach has been developed by the authors and has become an interesting research area in applied mathematics and physics. The book can be used as a concise introduction to quantum probability from an algebraic aspect. Here readers will learn several powerful methods and techniques of wide applicability, which have been recently developed under the name of quantum probability. The exercises at the end of each chapter help to deepen understanding.
Among the topics discussed along the way are: quantum probability and orthogonal polynomials; asymptotic spectral theory (quantum central limit theorems) for adjacency matrices; the method of quantum decomposition; notions of independence and structure of graphs; and asymptotic representation theory of the symmetric groups.
Content:
Front Matter....Pages I-XVIII
Quantum Probability and Orthogonal Polynomials....Pages 1-63
Adjacency Matrices....Pages 65-83
Distance-Regular Graphs....Pages 85-103
Homogeneous Trees....Pages 105-130
Hamming Graphs....Pages 131-146
Johnson Graphs....Pages 147-173
Regular Graphs....Pages 175-203
Comb Graphs and Star Graphs....Pages 205-247
The Symmetric Group and Young Diagrams....Pages 249-270
The Limit Shape of Young Diagrams....Pages 271-296
Central Limit Theorem for the Plancherel Measures of the Symmetric Groups....Pages 297-320
Deformation of Kerov's Central Limit Theorem....Pages 321-350
Back Matter....Pages 351-373
This is the first book to comprehensively cover the quantum probabilistic approach to spectral analysis of graphs. This approach has been developed by the authors and has become an interesting research area in applied mathematics and physics. The book can be used as a concise introduction to quantum probability from an algebraic aspect. Here readers will learn several powerful methods and techniques of wide applicability, which have been recently developed under the name of quantum probability. The exercises at the end of each chapter help to deepen understanding.
Among the topics discussed along the way are: quantum probability and orthogonal polynomials; asymptotic spectral theory (quantum central limit theorems) for adjacency matrices; the method of quantum decomposition; notions of independence and structure of graphs; and asymptotic representation theory of the symmetric groups.
Content:
Front Matter....Pages I-XVIII
Quantum Probability and Orthogonal Polynomials....Pages 1-63
Adjacency Matrices....Pages 65-83
Distance-Regular Graphs....Pages 85-103
Homogeneous Trees....Pages 105-130
Hamming Graphs....Pages 131-146
Johnson Graphs....Pages 147-173
Regular Graphs....Pages 175-203
Comb Graphs and Star Graphs....Pages 205-247
The Symmetric Group and Young Diagrams....Pages 249-270
The Limit Shape of Young Diagrams....Pages 271-296
Central Limit Theorem for the Plancherel Measures of the Symmetric Groups....Pages 297-320
Deformation of Kerov's Central Limit Theorem....Pages 321-350
Back Matter....Pages 351-373
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