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Combinatorial properties of non-crossing partitions, including the Möbius function play a central role in introducing free probability.
Free independence is defined via free cumulants in analogy with the way classical independence can be defined via classical cumulants.
Free cumulants are introduced through the Möbius function.
Free product probability spaces are constructed using free cumulants.
Marginal and joint tracial convergence of large dimensional random matrices such as the Wigner, elliptic, sample covariance, cross-covariance, Toeplitz, Circulant and Hankel are discussed.
Convergence of the empirical spectral distribution is discussed for symmetric matrices.
Asymptotic freeness results for random matrices, including some recent ones, are discussed in detail. These clarify the structure of the limits for joint convergence of random matrices.
Asymptotic freeness of independent sample covariance matrices is also demonstrated via embedding into Wigner matrices.
Exercises, at advanced undergraduate and graduate level, are provided in each chapter.
Combinatorial properties of non-crossing partitions, including the Möbius function play a central role in introducing free probability.
Free independence is defined via free cumulants in analogy with the way classical independence can be defined via classical cumulants.
Free cumulants are introduced through the Möbius function.
Free product probability spaces are constructed using free cumulants.
Marginal and joint tracial convergence of large dimensional random matrices such as the Wigner, elliptic, sample covariance, cross-covariance, Toeplitz, Circulant and Hankel are discussed.
Convergence of the empirical spectral distribution is discussed for symmetric matrices.
Asymptotic freeness results for random matrices, including some recent ones, are discussed in detail. These clarify the structure of the limits for joint convergence of random matrices.
Asymptotic freeness of independent sample covariance matrices is also demonstrated via embedding into Wigner matrices.
Exercises, at advanced undergraduate and graduate level, are provided in each chapter.
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.[...] 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).
- Classical independence, moments and cumulants. 2. Non-commutative probability. 3. Free independence. 4. Convergence. 5. Transforms. 6. C* -probability space. 7. Random matrices. 8. Convergence of some important matrices. 9. Joint convergence I: single pattern. 10. Joint convergence II: multiple patterns. 11. Asymptotic freeness of random matrices. 12. Brown measure. 13. Tying three loose ends.
| Erscheinungsjahr: | 2021 |
|---|---|
| Fachbereich: | Wahrscheinlichkeitstheorie |
| Genre: | Importe, Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| ISBN-13: | 9780367700812 |
| ISBN-10: | 0367700816 |
| Sprache: | Englisch |
| Einband: | Gebunden |
| Autor: | Bose, Arup |
| Hersteller: | Chapman and Hall/CRC |
| Verantwortliche Person für die EU: | Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de |
| Maße: | 240 x 161 x 20 mm |
| Von/Mit: | Arup Bose |
| Erscheinungsdatum: | 27.10.2021 |
| Gewicht: | 0,599 kg |
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.[...] 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).
- Classical independence, moments and cumulants. 2. Non-commutative probability. 3. Free independence. 4. Convergence. 5. Transforms. 6. C* -probability space. 7. Random matrices. 8. Convergence of some important matrices. 9. Joint convergence I: single pattern. 10. Joint convergence II: multiple patterns. 11. Asymptotic freeness of random matrices. 12. Brown measure. 13. Tying three loose ends.
| Erscheinungsjahr: | 2021 |
|---|---|
| Fachbereich: | Wahrscheinlichkeitstheorie |
| Genre: | Importe, Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| ISBN-13: | 9780367700812 |
| ISBN-10: | 0367700816 |
| Sprache: | Englisch |
| Einband: | Gebunden |
| Autor: | Bose, Arup |
| Hersteller: | Chapman and Hall/CRC |
| Verantwortliche Person für die EU: | Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de |
| Maße: | 240 x 161 x 20 mm |
| Von/Mit: | Arup Bose |
| Erscheinungsdatum: | 27.10.2021 |
| Gewicht: | 0,599 kg |
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