Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2013
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/1305.2611 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Inhaltsangabe:
- 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.