컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0119 |
|---|---|
| 분류(Section) | Poster Session |
| 분과(Session) | (AN) Analysis (AN) |
| 발표시간(Time) | 19th-B-14:00 -- 14:30 |
| 영문제목 (Title(Eng.)) |
Asymptotic freeness and a central limit theorem for partial transposes of Wishart matrices |
| 저자(Author(s)) |
Gyunam Park1, Sang-Gyun Youn1 Seoul National University1 |
| 초록본문(Abstract) | Mingo and Popa revealed asymptotic freeness between partial transposes of the Wishart matrices in bipartite situations. This poster is about a follow-up study in the multipartite situation. In $n$-partite system, we can extract particular permutations $\mathcal{E}_{1}, \cdots, \mathcal{E}_{n}$ on $[\pm m]$ from given word with length $m$ composed of partial transposes. Mingo and Popa reached their conclusion via combinatorial arguments about $\mathcal{E}_{1}$ and $\mathcal{E}_{2}$. By employing new combinatorial technics and sharper estimates, we have generalized their results to the multipartite systems, even in a stronger sense of almost sure convergence. Moreover, we exhibit a free central limit theorem for the partial transposes in the asymptotic situation. |
| 분류기호 (MSC number(s)) |
46L54 |
| 키워드(Keyword(s)) | Asymptotic freeness, central limit theorem, Wishart random matrix |
| 강연 형태 (Language of Session (Talk)) |
Korean |