# Random right eigenvalues of Gaussian quaternionic matrices

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Abstract : 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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2011
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Cited literature [11 references]

https://hal.archives-ouvertes.fr/hal-00587958
Contributor : Francois Chapon <>
Submitted on : Friday, September 2, 2011 - 10:32:18 AM
Last modification on : Thursday, April 27, 2017 - 9:46:25 AM
Document(s) archivé(s) le : Saturday, December 3, 2011 - 2:22:39 AM

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### Identifiers

• HAL Id : hal-00587958, version 2
• ARXIV : 1104.4455

### Citation

Florent Benaych-Georges, Francois Chapon. Random right eigenvalues of Gaussian quaternionic matrices. 2011. 〈hal-00587958v2〉

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