Random Right Eigenvalues of Gaussian Quaternionic Matrices

Random Matrices: Theory and Application

Volumn 1, Issue 2, 2012, Pages

  Benaych Georges, Florent ^a,b   Chapon, François ^c  

^a SORBONNE UNIVERSITÉ   (France)

^b CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

^c TELECOM PARISTECH   (France)

Author keywords

quaternions; Random matrices

Indexed keywords

EID: 85018104182     PISSN: 20103263     EISSN: 20103271     Source Type: Journal    
DOI: 10.1142/S2010326311500092     Document Type: Article

References (13)

1. G. Anderson, A. Guionnet and O. Zeitouni, An Introduction to Random Matrices, Cambridge Studies in Advanced Mathematics, Vol. 118 (2009).
2. G. Ben Arous and A. Guionnet, Large deviations for Wigner's law and Voiculescu's non-commutative entropy, Probab. Theory Related Fields 108(4) (1997) 517-542.
3. G. Ben Arous and O. Zeitouni, Large deviations from the circular law, ESAIM Probab. Statist. 2 (1998) 123-134.
4. F. Benaych-Georges and T. Lévy, A continuous semigroup of notions of independence between the classical and the free one, Ann. Probab. 39(3) (2011) 904-938.
5. J. L. Brenner, Matrices of quaternions, Pacific J. Math. 1 (1951) 329-335.
6. P. A. Deift, Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach, Courant Lecture Notes in Mathematics, Vol. 3 (New York University Courant Institute of Mathematical Sciences, New York, 1999).
7. J. Ginibre, Statistical ensembles of complex, quaternion, and real matrices, J. Math. Phys. 6(3) (1965) 440-449.
8. K. Johansson, On fluctuations of eigenvalues ofRandom Hermitian matrices, Duke Math. J. 91(1) (1998) 151-204.
9. M. L. Mehta,Random Matrices, third edn., Pure and Applied Mathematics (Amsterdam), Vol. 142 (Elsevier/Academic Press, Amsterdam, 2004).
10. E. B. Saff and V. Totik, Logarithmic Potentials with External Fields (Springer-Verlag, 1997).
11. T. Tao, V. Vu and M. KrishnapurRandom matrices: Universality of ESDs and the circular law, Ann. Probab. 38(5) (2010) 2023-2065.
12. E. Wigner, On the distribution of the roots of certain symmetric matrices, Ann. Math. 67 (1958) 325-327.
13. F. Zhang, Quaternions and matrices of quaternions, Linear Algebra Appl. 251 (1997) 21-57.