| Description |
1 online resource (213 pages) |
| Contents |
Cover; Half Title; Title Page; Copyright Page; Dedication; Table of Contents; Preface; About the Authors; Introduction; 1: Circulants; 1.1 Circulant; 1.2 Symmetric circulant; 1.3 Reverse circulant; 1.4 k-circulant; 1.5 Exercises; 2: Symmetric and reverse circulant; 2.1 Spectral distribution; 2.2 Moment method; 2.2.1 Scaling; 2.2.2 Input and link; 2.2.3 Trace formula and circuits; 2.2.4 Words and vertices; 2.2.5 (M1) and Riesz's condition; 2.2.6 (M4) condition; 2.3 Reverse circulant; 2.4 Symmetric circulant; 2.5 Related matrices; 2.6 Reduced moment; 2.6.1 A metric; 2.6.2 Minimal condition |
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2.7 Exercises3: LSD: normal approximation; 3.1 Method of normal approximation; 3.2 Circulant; 3.3 k-circulant; 3.4 Exercises; 4: LSD: dependent input; 4.1 Spectral density; 4.2 Circulant; 4.3 Reverse circulant; 4.4 Symmetric circulant; 4.5 k-circulant; 4.6 Exercises; 5: Spectral radius: light tail; 5.1 Circulant and reverse circulant; 5.2 Symmetric circulant; 5.3 Exercises; 6: Spectral radius: k-circulant; 6.1 Tail of product; 6.2 Additional properties of the k-circulant; 6.3 Truncation and normal approximation; 6.4 Spectral radius of the k-circulant; 6.4.1 k-circulant for sn = kg + 1 |
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6.5 Exercises7: Maximum of scaled eigenvalues: dependent input; 7.1 Dependent input with light tail; 7.2 Reverse circulant and circulant; 7.3 Symmetric circulant; 7.4 k-circulant; 7.4.1 k-circulant for n = k2 + 1; 7.4.2 k-circulant for n = kg + 1, g> 2; 7.5 Exercises; 8: Poisson convergence; 8.1 Point process; 8.2 Reverse circulant; 8.3 Symmetric circulant; 8.4 k-circulant, n = k2 + 1; 8.5 Reverse circulant: dependent input; 8.6 Symmetric circulant: dependent input; 8.7 k-circulant, n = k2 + 1: dependent input; 8.8 Exercises; 9: Heavy-tailed input: LSD |
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9.1 Stable distribution and input sequence9.2 Background; 9.3 Reverse circulant and symmetric circulant; 9.4 k-circulant: n = kg + 1; 9.4.1 Proof of Theorem 9.4.2; 9.5 k-circulant: n = kg -- 1; 9.6 Tail of the LSD; 9.7 Exercises; 10: Heavy-tailed input: spectral radius; 10.1 Input sequence and scaling; 10.2 Reverse circulant and circulant; 10.3 Symmetric circulant; 10.4 Heavy-tailed: dependent input; 10.5 Exercises; 11: Appendix; 11.1 Proof of Theorem 1.4.1; 11.2 Standard notions and results; 11.3 Three auxiliary results; Bibliography; Index |
| Notes |
Print version record |
| Subject |
Eigenvalues -- Problems, exercises, etc
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Matrices -- Problems, exercises, etc
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Random matrices -- Problems, exercises, etc
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Eigenvalues
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Matrices
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Random matrices
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| Genre/Form |
Problems and exercises
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| Form |
Electronic book
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| Author |
Saha, Koushik
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| ISBN |
9780429788192 |
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0429788193 |
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