Random matrices with complex Gaussian entries

By Uffe Haagerup, S. Thorbjørnsen. 2003

200 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/bf9f274e82273116c450867d2b34ef5ed4eb89f6

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In Mathematical Physics

In Statistics and Probability

Citations in the corpus

All Invariant Moments of the Wishart Distribution (2004, background): “…understood yet for other values of d. Letac & Massam (2001) give an analogue to theorem 1 for an arbitrary Jordan algebra V by replacing rp by another closely related k linear form Rp on V. Interesting information about the complex case can be found in section 5 of Haagerup & Thorbjørnsen (1998).”
Annular noncrossing permutations and partitions, and second-order asymptotics for random matrices (2003, background): “,X (k) s converges in distribution to the Marcenko-Pastur distribution (for a nice presentation of this, see the Section 6 of [6]).”
Multimode antenna selection for spatial multiplexing systems with linear receivers (2005, methodology): “For the complex Gaussian case distribution, relying on results from [15,18]”
A Linearization of Connes' Embedding Problem (2007, background): “7) and the next displayed equation of [10]), we have (55) lim N→∞ Prob(c · 1 ≤ AN ≤ d · 1) = 1, and also for BN .”
Lectures on the Combinatorics of Free Probability (2006, background): “For more information and references we refer to the recent surveys [29, 34, 37, 77].”
Non-commutative polynomials of independent Gaussian random matrices. The real and symplectic cases. (2003, background): “Then for all " > 0 we have (cf. [ HT1 , Proof of Lemma 3.3])”
A new application of random matrices: Ext(C^*_{red}(F_2)) is not a group (2002, background): “[BY], [Ba, Thm. 2.12] or [ HT1 , Thm. 3.1]). From Theorem A above, it is not hard to obtain the following result (cf.”
Strong asymptotic freeness for Wigner and Wishart matrices preprint (2005, result): “1 of [9], using previous results in [8].”
Large Deviations Upper Bounds for the Laws of Matrix-Valued Processes and Non-Communicative Entropies (2001, background): “To control the above bound, let us invoke the result of [19] which says that for any integer number N there exists a polynomial function BN so that for any y ∈ ,”