New York Journal of Mathematics
Volume 14 (2008) 617-641


Benoît Collins and Ken Dykema

A linearization of Connes' embedding problem

Published: October 30, 2008
Keywords: Connes Embedding Problem, Horn Problem, random matrices, free probability, sum of matrices
Subject: 46L10,15A42

We show that Connes' embedding problem for II1-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.


The first author's research was supported in part by NSERC grant RGPIN/341303-2007
The second author's research was supported in part by NSF grant DMS-0600814

Author information

Benoît Collins:
Department of Mathematics and Statistics, University of Ottawa, 585 King Edward, Ottawa, ON K1N 6N5 Canada, and CNRS, Department of Mathematics, Lyon 1 Claude Bernard University

Ken Dykema:
Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA