COMBINATORIAL ASPECTS OF CONNES'S EMBEDDING CONJECTURE AND ASYMPTOTIC DISTRIBUTION OF TRACES OF PRODUCTS OF UNITARIES

By Florin Radulescu. 2004

54 citations recorded by the source corpus.

In this paper we study the asymptotic distribution of the moments of (nonnormalized) traces Tr(w1),Tr(w2), . . . ,Tr(wr), where w1,w2, . . . ,wr are reduced words in unitaries in the group U(N). We prove that as N → ∞ these variables are distributed as normal gaussian variables √j1Z1, . . . ,√Zr, where j1, . . . , jr are the number of cyclic rotations of the words w1, . . . ,ws leaving them invariant. This extends a previous result by Diaconis ([4]), where this it was proved, that Tr(U),Tr(U2), . . . , Tr(Up) are asymptotically distributed as Z1,√2Z2, . . . ,√pZp. We establish a combinatorial formula for R |Tr(w1)|2 · · · |Tr(wp)|2. In our computation we reprove some results from [1].

Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/faeab5206513347b210c00d98cdbfb0a232b6b04

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In Discrete Mathematics and Combinatorics

1. Kate Juschenko
2. K. Dykema
3. Roland Speicher
4. D. Voiculescu
5. Alexandru Nica

In Mathematical Physics

1. Kate Juschenko
2. K. Dykema
3. Nathanial P. Brown Narutaka Ozawa
4. Gilles Pisier
5. Uffe Haagerup
6. Magdalena Musat
7. Volodymyr V. Nekrashevych

In Statistics and Probability

1. Kate Juschenko
2. K. Dykema
3. Roland Speicher
4. D. Voiculescu
5. Alexandru Nica

Citations in the corpus

• Matrices of unitary moments (2009, background): “(See also the survey [10], and the papers [11], [12], [13], [1], [14], [3], [7], [15], [5] for results with bearing on Connes’ embedding problem.)”
• A Linearization of Connes' Embedding Problem (2007, unknown): “O A ] 2 6 Ju n 20 07”