Affiliation:
1. Toronto, Ontario, Canada
Abstract
We present a definition for second-order freeness in the quaternionic case. We demonstrate that this definition on a second-order probability space is asymptotically satisfied by independent symplectically invariant quaternionic matrices. This definition is different from the natural definition for complex and real second-order probability spaces, those motivated by the asymptotic behavior of unitarily invariant and orthogonally invariant random matrices respectively. Most notably, because the quaternionic trace does not have the cyclic property of a trace over a commutative field, the asymmetries which appear in the multi-matrix context result in an asymmetric contribution from the terms which appear symmetrically in the complex and real cases.
Publisher
World Scientific Pub Co Pte Lt
Subject
Discrete Mathematics and Combinatorics,Statistics, Probability and Uncertainty,Statistics and Probability,Algebra and Number Theory
Cited by
3 articles.
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