Subordination of the resolvent for a sum of random matrices

Details Subordination of the resolvent for a sum of random matrices Subordination of the resolvent for a sum of random matrices

2011-09-27

arxiv.org/abs/1109.5818v1

Mathematics

Probability

19 pages

Scientific paper

This paper is about the relation of random matrix theory and the subordination phenomenon in complex analysis. Previously, subordination was discovered in free probability theory by Voiculescu (1993) and Biane (1998). We find that approximate subordination holds for certain ensembles of random matrices. This allows us to prove an improved local limit law for eigenvalues and a delocalization result for eigenvectors of these ensembles.

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