The Brown Measure of Non-Hermitian Sums of Projections
| Autor: | Zhou, Max Sun |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We compute the Brown measure of the non-normal operators $X = p + i q$, where $p$ and $q$ are Hermitian, freely independent, and have spectra consisting of $2$ atoms. The computation relies on the model of the non-trivial part of the von Neumann algebra generated by 2 projections as $2 \times 2$ random matrices. We observe that these measures are supported on hyperbolas and note some other properties related to their atoms and symmetries. Comment: 31 pages, 3 figures |
| Databáze: | arXiv |
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