Ebook: Asymptotic Combinatorics with Application to Mathematical Physics

New and striking results obtained in recent years from an intensive study of asymptotic combinatorics have led to a new, higher level of understanding of related problems: the theory of integrable systems, the Riemann-Hilbert problem, asymptotic representation theory, spectra of random matrices, combinatorics of Young diagrams and permutations, and even some aspects of quantum field theory.

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New and striking results obtained in recent years from an intensive study of asymptotic combinatorics have led to a new, higher level of understanding of related problems: the theory of integrable systems, the Riemann-Hilbert problem, asymptotic representation theory, spectra of random matrices, combinatorics of Young diagrams and permutations, and even some aspects of quantum field theory.

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New and striking results obtained in recent years from an intensive study of asymptotic combinatorics have led to a new, higher level of understanding of related problems: the theory of integrable systems, the Riemann-Hilbert problem, asymptotic representation theory, spectra of random matrices, combinatorics of Young diagrams and permutations, and even some aspects of quantum field theory.
Content:
Front Matter....Pages i-xv
Front Matter....Pages 1-1
Matrix Quantum Mechanics....Pages 3-21
Introduction to Matrix Models....Pages 23-50
A Class of the Multi-Interval Eigenvalue Distributions of Matrix Models and Related Structures....Pages 51-70
Combinatorics and Probability of Maps....Pages 71-95
The Combinatorics of Alternating Tangles: From Theory to Computerized Enumeration....Pages 97-112
Invariance Principles for Non-Uniform Random Mappings and Trees....Pages 113-147
Front Matter....Pages 149-149
Renormalization Group Solution of Fermionic Dyson Model....Pages 151-166
Statistical Mechanics and Number Theory....Pages 167-208
Quantization of Thermodynamics and the Bardeen-Cooper-Schriffer-Bogolyubov Equation....Pages 209-220
Approximate Distribution of Hitting Probabilities for a Regular Surface with Compact Support in 2D....Pages 221-242
Front Matter....Pages 243-243
Notes on Homogeneous Vector Bundles over Complex Flag Manifolds....Pages 245-254
Representations Theory and Doubles of Yangians of Classical Lie Superalgebras....Pages 255-265
Idempotent (Asymptotic) Mathematics and the Representation Theory....Pages 267-278
A New Approach to Berezin Kernels and Canonical Representations....Pages 279-305
Theta Hypergeometric Series....Pages 307-327

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New and striking results obtained in recent years from an intensive study of asymptotic combinatorics have led to a new, higher level of understanding of related problems: the theory of integrable systems, the Riemann-Hilbert problem, asymptotic representation theory, spectra of random matrices, combinatorics of Young diagrams and permutations, and even some aspects of quantum field theory.
Content:
Front Matter....Pages i-xv
Front Matter....Pages 1-1
Matrix Quantum Mechanics....Pages 3-21
Introduction to Matrix Models....Pages 23-50
A Class of the Multi-Interval Eigenvalue Distributions of Matrix Models and Related Structures....Pages 51-70
Combinatorics and Probability of Maps....Pages 71-95
The Combinatorics of Alternating Tangles: From Theory to Computerized Enumeration....Pages 97-112
Invariance Principles for Non-Uniform Random Mappings and Trees....Pages 113-147
Front Matter....Pages 149-149
Renormalization Group Solution of Fermionic Dyson Model....Pages 151-166
Statistical Mechanics and Number Theory....Pages 167-208
Quantization of Thermodynamics and the Bardeen-Cooper-Schriffer-Bogolyubov Equation....Pages 209-220
Approximate Distribution of Hitting Probabilities for a Regular Surface with Compact Support in 2D....Pages 221-242
Front Matter....Pages 243-243
Notes on Homogeneous Vector Bundles over Complex Flag Manifolds....Pages 245-254
Representations Theory and Doubles of Yangians of Classical Lie Superalgebras....Pages 255-265
Idempotent (Asymptotic) Mathematics and the Representation Theory....Pages 267-278
A New Approach to Berezin Kernels and Canonical Representations....Pages 279-305
Theta Hypergeometric Series....Pages 307-327
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