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Free Probability/Non-commutative Probability has gained much attentionsignificant advances have been made since its initiation in the 1990's. Though it started as a branch of Mathematics, it has found significant applications in statistics, wireless communication etc, particularly through deep and interesting connections with Random Matrix Theory.
List of contents
- 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.
About the author
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).
Summary
Free Probability/Non-commutative Probability has gained much attentionsignificant advances have been made since its initiation in the 1990’s. Though it started as a branch of Mathematics, it has found significant applications in statistics, wireless communication etc, particularly through deep and interesting connections with Random Matrix Theory.
