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Topics in Random Matrix Theory
Abstract
The field of random matrix theory has seen an explosion of activity in recent years, with connections to many areas of mathematics and physics. However, this makes the current state of the field almost too large to survey in a single book. In this graduate text, we focus on one specific sector of the field, namely the spectral distribution of random Wigner matrix ensembles (such as the Gaussian Unitary Ensemble), as well as iid matrix ensembles. The text is largely self-contained and starts with a review of relevant aspects of probability theory and linear algebra. With over 200 exercises, the book is suitable as an introductory text for beginning graduate students seeking to enter the field.
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Cited by
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Hastie, T., Montanari, A., Rosset, S., & Tibshirani, R. J. (2022) · The Annals of Statistics · doi:10.1214/21-aos2133 · Cited by 503
Hanson-Wright inequality and sub-gaussian concentration
Rudelson, M., & Vershynin, R. (2013) · Electronic Communications in Probability · doi:10.1214/ecp.v18-2865 · Cited by 502
A Universal Operator Growth Hypothesis
Parker, D. E., Cao, X., Avdoshkin, A., Scaffidi, T., & Altman, E. (2019) · Physical Review X · doi:10.1103/physrevx.9.041017 · Cited by 367
Chaos, complexity, and random matrices
Cotler, J., Hunter-Jones, N., Liu, J., & Yoshida, B. (2017) · Journal of High Energy Physics · doi:10.1007/jhep11(2017)048 · Cited by 264
Topological and Dynamical Complexity of Random Neural Networks
Wainrib, G., & Touboul, J. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.118101 · Cited by 124
Metadata
- Authors
- Tao, T.
- Venue
- Graduate Studies in Mathematics
- Publisher
- American Mathematical Society
- Published
- 2012-03-21
- ISSN
- 1065-7339 (ISSN-L)
- OpenAlex
- W602904462
- Cited by
- 868
- References
- 0
- FWCI
- 13.65
- Type
- book
- Language
- en
- Open access
- closed
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