A Linearization of Connes' Embedding Problem

By Benoît Collins, K. Dykema. 2007

64 citations recorded by the source corpus.

We show that Connes' embedding problem for II_1-factors is equivalent to a statement about distributions of sums of self-adjoint operators with matrix coefficients. This is an application of a linearization result for finite von Neumann algebras, which is proved using asymptotic second order freeness of Gaussian random matrices.

View Paper: https://www.semanticscholar.org/paper/4fa3c958d0aed4dcde0113669bfcc37cc4fb8faa

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Citations in the corpus

Grothendieck's Theorem, past and present (2011, unknown): “See [131, 132, 33, 66, 37, 25] for related contributions.”
Asymptotics of unitary and orthogonal matrix integrals (2006, background): “Indeed, this implies that Tr ( [9] Lemma 2.9 for a probabilistic proof or [22], Proposition 2.3 for a direct proof (in the real symmetric case, but directly adaptable to the Hermitian case).”
Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture (2013, unknown): “Following the aforementioned papers by Voiculescu and Kirchberg, a series of papers from different authors proving various equivalent reformulations of Connes’ embedding conjecture appeared, such as [8],[90], [28], [63], [46] contributing to arouse the interest around”