Random matrices and non-commutative probability /
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| Author / Creator: | Bose, Arup, author. |
|---|---|
| Edition: | First edition. |
| Imprint: | Boca Raton, FL : CRC Press, 2022. ©2022 |
| Description: | 1 online resource ( xxii, 264 pages) |
| Language: | English |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/12770740 |
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| 100 | 1 | |a Bose, Arup, |e author. | |
| 245 | 1 | 0 | |a Random matrices and non-commutative probability / |c Arup Bose. |
| 250 | |a First edition. | ||
| 264 | 1 | |a Boca Raton, FL : |b CRC Press, |c 2022. | |
| 264 | 4 | |c ©2022 | |
| 300 | |a 1 online resource ( xxii, 264 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 504 | |a Includes bibliographical references and index. | ||
| 545 | 0 | |a Arup Bose is on the faculty of the Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, Kolkata, India. He has research contributions in statistics, probability, economics and econometrics. He is a Fellow of the Institute of Mathematical Statistics (USA), and of all three national science academies of India. He is a recipient of the S.S. Bhatnagar Prize and the C.R. Rao Award and holds a J.C. Bose National Fellowship. He has been on the editorial board of several journals. He has authored four books: Patterned Random Matrices, Large Covariance and Autocovariance Matrices (with Monika Bhattacharjee), U-Statistics, Mm-Estimators and Resampling (with Snigdhansu Chatterjee) and Random Circulant Matrices (with Koushik Saha). | |
| 505 | 0 | |a Classical independence, moments and cumulants Classical independence CLT a cumulants Cumulants to moments Moments to cumulants, the Möbius function Classical Isserlis' formula Exercises Non-commutative probability Non-crossing partition Free cumulants Free Gaussian or semi-circle law Free Poisson law Non-commutative and *-probability spaces Moments and probability laws of variables Exercises Free independence Free independence Free product of *-probability spaces Free binomial Semi-circular family Free Isserlis' formula Circular and elliptic variables Free additive convolution Kreweras complement Moments of free variables 0 Compound free Poisson Exercises Convergence Algebraic convergence Free central limit theorem Free Poisson convergence Sums of triangular arrays Exercises Transforms Stieltjes transform R transform Interrelation S-transform Free infinite divisibility Exercises C* -probability space C* -probability space Spectrum Distribution of a self-adjoint element Free product of C* -probability spaces Free additive and multiplicative convolution Exercises Random matrices Empirical spectral measure Limiting spectral measure Moment and trace Some important matrices A unified treatment Exercises Convergence of some important matrices Wigner matrix: semi-circle law S-matrix: Marcenko-Pastur law IID and elliptic matrices: circular and elliptic variables Toeplitz matrix Hankel matrix Reverse Circulant matrix: symmetrized Rayleigh law Symmetric Circulant: Gaussian law Almost sure convergence of the ESD Exercises Joint convergence I: single pattern Unified treatment: extension Wigner matrices: asymptotic freeness Elliptic matrices: asymptotic freeness S-matrices in elliptic models: asymptotic freeness Symmetric Circulants: asymptotic independence Reverse Circulants: asymptotic half independence Exercises Joint convergence II: multiple patterns Multiple patterns: colors and indices Joint convergence Two or more patterns at a time Sum of independent patterned matrices Discussion Exercises Asymptotic freeness of random matrices Elliptic, IID, Wigner, and S-matrices Gaussian elliptic, IID, Wigner and deterministic matrices General elliptic, IID, Wigner, and deterministic matrices S-matrices and embedding Cross covariance matrices Pair-correlated cross-covariance; p/n ! y Pair correlated cross covariance; p/n ! Wigner and patterned random matrices Discussion Exercises Brown measure Brown measure Exercises Tying three loose ends Möbius function on NC(n) Equivalence of two freeness definitions Free product construction Exercises Bibliography Index | |
| 588 | 0 | |a Online resource; title from digital title page (viewed on November 29, 2021). | |
| 650 | 0 | |a Random matrices. | |
| 650 | 0 | |a Free probability theory. | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x General. |2 bisacsh | |
| 650 | 7 | |a Free probability theory. |2 fast |0 (OCoLC)fst00933913 | |
| 650 | 7 | |a Random matrices. |2 fast |0 (OCoLC)fst01089803 | |
| 776 | 0 | 8 | |i Print version: |z 0367700816 |z 9780367700812 |w (OCoLC)1248897352 |
| 856 | 4 | 0 | |u https://www.taylorfrancis.com/books/9781003144496 |y Taylor & Francis eBooks |x 999 |
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| 928 | |t Library of Congress classification |a QA196.5.B67 2022 |l Online |c UC-FullText |u https://www.taylorfrancis.com/books/9781003144496 |z Taylor & Francis eBooks |g ebooks |e CORA |i 12908251 | ||