Patterned random matrics / Arup Bose.

Author/creator Bose, Arup
Format Electronic
Publication InfoBoca Raton, FL : CRC Press, an imprint of the Taylor & Francis Group, [2018]
Descriptionpages cm
Supplemental ContentFull text available from Taylor & Francis eBooks
Subjects
Random matrices.
Probabilities.

Contents A unified framework -- Empirical and limiting spectral distribution -- Moment method -- A metric for probability measures -- Patterned matrices: a unified approach -- Scaling -- Reduction to bounded case -- Trace formula and circuits -- Words -- Vertices -- Pair-matched word -- Sub-sequential limit -- Exercises -- Common symmetric patterned matrices -- Wigner matrix -- Semi-circle law, non-crossing partitions, catalan words -- LSD -- Toeplitz and Hankel matrices -- Toeplitz matrix -- Hankel matrix -- Reverse circulant matrix -- Symmetric circulant and related matrices -- Additional properties of the LSD -- Moments of Toeplitz and Hankel LSD -- Contribution of words and comparison of LSD -- Unbounded support of Toeplitz and Hankel LSD -- Non-unimodality of Hankel LSD -- Density of Toeplitz LSD -- Pyramidal multiplicativity -- Exercises -- Patterned XX matrices -- A unified set up -- Aspect ratio y = -- Preliminaries -- Sample variance-covariance matrix -- Catalan words and Marchenko-Pastur law -- LSD -- Other XX matrices -- Aspect ratio y = -- Sample variance-covariance matrix -- Other XX matrices -- Exercises -- K-circulant matrices -- Normal approximation -- Circulant matrix -- K-circulant matrices -- Eigenvalues -- Eigenvalue partition -- Lower order elements -- Degenerate limit -- Non-degenerate limit -- Exercises -- Wigner type matrices -- Wigner-type matrix -- Exercises -- Balanced Toeplitz and Hankel matrices -- Main results -- Exercises -- Patterned band matrices -- LSD for band matrices -- Proof -- Reduction to uniformly bounded input -- Trace formula, circuits, words and matches -- Negligibility of higher order edges -- (m) condition -- Exercises -- Triangular matrices -- General pattern -- Triangular Wigner matrix -- LSD -- Contribution of catalan words -- Exercises -- Joint convergence of iid patterned matrices -- Non-commutative probability space -- Joint convergence -- Nature of the limit -- Exercises -- Joint convergence of independent patterned matrices -- Definitions and notation -- Joint convergence -- Freeness -- Sum of independent patterned matrices -- Proofs -- Exercises -- Autocovariance matrix -- Preliminaries -- Main results -- Proofs -- Exercises.
Abstract "This book focuses on the limit spectral distribution (LSD) of patterned random matrices and provides a comprehensive variety of LSD results. It is accessible to first or second years Master's students and uses very elementary techniques. It is suitable for a beginner in random matrices with some probability background"-- Provided by publisher.
Access restrictionAvailable only to authorized users.
Technical detailsMode of access: World Wide Web
Genre/formElectronic books.
LCCN 2018010540
ISBN9781138591462 (hardback)
ISBNebook

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