Asymptotically liberating sequences of random unitary matrices
| Autor: | Brendan Farrell, Greg W. Anderson |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Mathematics::Operator Algebras
Higher-dimensional gamma matrices General Mathematics Probability (math.PR) Mathematics - Operator Algebras Unitary matrix Free probability Combinatorics Complex Hadamard matrix Hadamard transform FOS: Mathematics Operator Algebras (math.OA) 46L54 60B20 15B52 42A61 Random matrix Circular ensemble Mathematics - Probability Mathematics |
| Zdroj: | Advances in Mathematics. 255:381-413 |
| ISSN: | 0001-8708 |
| Popis: | A fundamental result of free probability theory due to Voiculescu and subsequently refined by many authors states that conjugation by independent Haar-distributed random unitary matrices delivers asymptotic freeness. In this paper we exhibit many other systems of random unitary matrices that, when used for conjugation, lead to freeness. We do so by first proving a general result asserting "asymptotic liberation" under quite mild conditions, and then we explain how to specialize these general results in a striking way by exploiting Hadamard matrices. In particular, we recover and generalize results of the second-named author and of Tulino-Caire-Shamai-Verd\'{u}. Comment: 26 pages, no figures, LaTeX. In v2, Prop. 2.6 and its proof were corrected, and the proof of Cor. 3.4 was correspondingly modified. In v3, typos were corrected, a corollary was added, extra details and explanations were added, and the proof of Cor. 3.4 (now Cor. 3.7) was rewritten. In v4 (this version) light editing and new reference added |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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