Random right eigenvalues of Gaussian quaternionic matrices

Details Random right eigenvalues of Gaussian quaternionic matrices Random right eigenvalues of Gaussian quaternionic matrices

2011-04-22

arxiv.org/abs/1104.4455v2

Mathematics

Probability

Scientific paper

We consider a random matrix whose entries are independent Gaussian variables taking values in the field of quaternions with variance $1/n$. Using logarithmic potential theory, we prove the almost sure convergence, as the dimension $n$ goes to infinity, of the empirical distribution of the right eigenvalues towards some measure supported on the unit ball of the quaternions field. Some comments on more general Gaussian quaternionic random matrix models are also made.

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