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Proceedings of the London Mathematical Society Advance Access published online on June 9, 2009
Proceedings of the London Mathematical Society, doi:10.1112/plms/pdp021
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© 2009 London Mathematical Society

Spectral properties of matrices associated with some directed graphs

E. B. Davies

Department of Mathematics
King's College London
Strand
London
WC2R 2LS
United Kingdom

P. A. Incani

Department of Mathematics
King's College London
Strand
London
WC2R 2LS
United Kingdom
Paul.Incani@kcl.ac.uk

Received 11 February 2008. Revision received 3 March 2009.

We study the spectral properties of certain non-self-adjoint matrices associated with large directed graphs. Asymptotically the eigenvalues converge to certain curves, apart from a finite number that have limits not on these curves.

2000 Mathematics Subject Classification 34L20 (primary), 30C15 (secondary).

The second author would like to thank King's College London for financially supporting his PhD.


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