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| Format: | Preprint |
| Published: |
2013
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| Online Access: | https://arxiv.org/abs/1305.2611 |
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| _version_ | 1866908405153660928 |
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| author | Kargin, Vladislav |
| author_facet | Kargin, Vladislav |
| contents | These lecture notes provide an introduction to free probability theory, with a focus on tools and techniques useful in the study of large random matrices. Topics include freeness, free cumulants, additive and multiplicative free convolution, the R- and S-transforms, subordination theory, and operator-valued extensions. Applications to asymptotic freeness and linearization methods are discussed in detail. The notes aim to be accessible to graduate students with a background in functional analysis and probability.
The lecture notes were originally written for a graduate course. They are updated to include recent results on subordination and linearization methods in free probability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1305_2611 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | Lecture Notes on Free Probability Kargin, Vladislav Probability 46L54 These lecture notes provide an introduction to free probability theory, with a focus on tools and techniques useful in the study of large random matrices. Topics include freeness, free cumulants, additive and multiplicative free convolution, the R- and S-transforms, subordination theory, and operator-valued extensions. Applications to asymptotic freeness and linearization methods are discussed in detail. The notes aim to be accessible to graduate students with a background in functional analysis and probability. The lecture notes were originally written for a graduate course. They are updated to include recent results on subordination and linearization methods in free probability. |
| title | Lecture Notes on Free Probability |
| topic | Probability 46L54 |
| url | https://arxiv.org/abs/1305.2611 |