Patterned Random Matrices. (2018)
- Record Type:
- Book
- Title:
- Patterned Random Matrices. (2018)
- Main Title:
- Patterned Random Matrices
- Further Information:
- Note: Arup Bose.
- Authors:
- Bose, Arup
- Contents:
- Cover; Half Title; Title; Copyright; Contents; Preface; Introduction; About the Author; Chapter 1 A unified framework; 1.1 Empirical and limiting spectral distribution; 1.2 Moment method; 1.3 A metric for probability measures; 1.4 Patterned matrices: A unified approach; 1.4.1 Scaling; 1.4.2 Reduction to bounded case; 1.4.3 Trace formula and circuits; 1.4.4 Words; 1.4.5 Vertices; 1.4.6 Pair-matched word; 1.4.7 Sub-sequential limit; 1.5 Exercises; Chapter 2 Common symmetric patterned matrices; 2.1 Wigner matrix; 2.1.1 Semi-circle law, non-crossing partitions, Catalan words; 2.1.2 LSD 2.2 Toeplitz and Hankel matrices2.2.1 Toeplitz matrix; 2.2.2 Hankel matrix; 2.3 Reverse Circulant matrix; 2.4 Symmetric Circulant and related matrices; 2.5 Additional properties of the LSDs; 2.5.1 Moments of the Toeplitz and Hankel LSDs; 2.5.2 Contribution of words and comparison of LSDs; 2.5.3 Unbounded support of the Toeplitz and Hankel LSDs; 2.5.4 Non-unimodality of the Hankel LSD; 2.5.5 Density of the Toeplitz LSD; 2.5.6 Pyramidal multiplicativity; 2.6 Exercises; Chapter 3 Patterned XX' matrices; 3.1 A unified setup; 3.2 Aspect ratio y = 0; 3.2.1 Preliminaries 3.2.2 Sample variance-covariance matrix3.2.2.1 Catalan words and the Marˇcenko-Pastur law; 3.2.2.2 LSD; 3.2.3 Other XX0 matrices; 3.3 Aspect ratio y = 0; 3.3.1 Sample variance-covariance matrix; 3.3.2 Other XX0 matrices; 3.4 Exercises; Chapter 4 k-Circulant matrices; 4.1 Normal approximation; 4.2 Circulant matrix; 4.3 k-CirculantCover; Half Title; Title; Copyright; Contents; Preface; Introduction; About the Author; Chapter 1 A unified framework; 1.1 Empirical and limiting spectral distribution; 1.2 Moment method; 1.3 A metric for probability measures; 1.4 Patterned matrices: A unified approach; 1.4.1 Scaling; 1.4.2 Reduction to bounded case; 1.4.3 Trace formula and circuits; 1.4.4 Words; 1.4.5 Vertices; 1.4.6 Pair-matched word; 1.4.7 Sub-sequential limit; 1.5 Exercises; Chapter 2 Common symmetric patterned matrices; 2.1 Wigner matrix; 2.1.1 Semi-circle law, non-crossing partitions, Catalan words; 2.1.2 LSD 2.2 Toeplitz and Hankel matrices2.2.1 Toeplitz matrix; 2.2.2 Hankel matrix; 2.3 Reverse Circulant matrix; 2.4 Symmetric Circulant and related matrices; 2.5 Additional properties of the LSDs; 2.5.1 Moments of the Toeplitz and Hankel LSDs; 2.5.2 Contribution of words and comparison of LSDs; 2.5.3 Unbounded support of the Toeplitz and Hankel LSDs; 2.5.4 Non-unimodality of the Hankel LSD; 2.5.5 Density of the Toeplitz LSD; 2.5.6 Pyramidal multiplicativity; 2.6 Exercises; Chapter 3 Patterned XX' matrices; 3.1 A unified setup; 3.2 Aspect ratio y = 0; 3.2.1 Preliminaries 3.2.2 Sample variance-covariance matrix3.2.2.1 Catalan words and the Marˇcenko-Pastur law; 3.2.2.2 LSD; 3.2.3 Other XX0 matrices; 3.3 Aspect ratio y = 0; 3.3.1 Sample variance-covariance matrix; 3.3.2 Other XX0 matrices; 3.4 Exercises; Chapter 4 k-Circulant matrices; 4.1 Normal approximation; 4.2 Circulant matrix; 4.3 k-Circulant matrices; 4.3.1 Eigenvalues; 4.3.2 Eigenvalue partition; 4.3.3 Lower-order elements; 4.3.4 Degenerate limit; 4.3.5 Non-degenerate limit; 4.4 Exercises; Chapter 5 Wigner-type matrices; 5.1 Wigner-type matrix; 5.2 Exercises Chapter 6 Balanced Toeplitz and Hankel matrices6.1 Main results; 6.2 Exercises; Chapter 7 Patterned band matrices; 7.1 LSD for band matrices; 7.2 Proof; 7.2.1 Reduction to uniformly bounded input; 7.2.2 Trace formula, circuits, words and matches; 7.2.3 Negligibility of higher-order edges; 7.2.4 (M1) condition; 7.3 Exercises; Chapter 8 Triangular matrices; 8.1 General pattern; 8.2 Triangular Wigner matrix; 8.2.1 LSD; 8.2.2 Contribution of Catalan words; 8.3 Exercises; Chapter 9 Joint convergence of i.i.d. patterned matrices; 9.1 Non-commutative probability space; 9.2 Joint convergence 9.3 Nature of the limit9.4 Exercises; Chapter 10 Joint convergence of independent patternedmatrices; 10.1 Definitions and notation; 10.2 Joint convergence; 10.3 Freeness; 10.4 Sum of independent patterned matrices; 10.5 Proofs; 10.6 Exercises; Chapter 11 Autocovariance matrix; 11.1 Preliminaries; 11.2 Main results; 11.3 Proofs; 11.4 Exercises; Bibliography; Index … (more)
- Publisher Details:
- Boca Raton, FL : CRC Press
- Publication Date:
- 2018
- Extent:
- 1 online resource
- Subjects:
- 512.9434
Probability Theory & Applications
Linear & Multilinear Algebra
Statistics & Probability
STATSnetBASE
MATHnetBASE
SCI-TECHnetBASE
STMnetBASE
Random matrices
Probabilities
Algebras, Linear
Multilinear algebra
Statistics
Electronic books
Electronic books - Languages:
- English
- ISBNs:
- 9780429488436
0429488432
9780429948893
0429948891
9780429948886
0429948883 - Related ISBNs:
- 1138591467
9781138591462 - Access Rights:
- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
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- British Library HMNTS - ELD.DS.287773
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