| |
|
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 |
|
|
Abstract
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.
|
|
| Acknowledgements
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
bcollins@uottawa.ca
Ken Dykema:
Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA
kdykema@math.tamu.edu
|
|
