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...

Ausführliche Beschreibung

Bibliographische Detailangaben

1. Verfasser:	Bose, Arup 1959- (VerfasserIn)
Format:	Elektronisch E-Book
Sprache:	English
Veröffentlicht:	Boca Raton ; London ; New York CRC Press [2018]
Schlagworte:	Stochastische Matrix Probabilities Random matrices Random variables Electronic books
Online-Zugang:	TUM01 Inhaltstext
Zusammenfassung:	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 matrices -- 2.2.1 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 matrix -- 3.2.2.1 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 matrices -- 6.1 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 limit -- 9.4 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
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ISBN:	9780429488436 9780429948886