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Random evolutions and the spectral radius of a non-negative matrix

Published online by Cambridge University Press:  24 October 2008

Joel E. Cohen
Joel E. Cohen
Affiliation:
The Rockefeller University, New York
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Extract

1. Introduction and summary. This paper offers yet another example of what probability theory can do for analysis. Using a Feynman-Kac formula derived in the theory of random evolutions (5), we find an expression (1) for the spectral radius r(A) of a finite square non-negative matrix A. This expression makes it very easy to study how r(A) behaves as a function of the diagonal elements of A.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 86 , Issue 2 , September 1979 , pp. 345 - 350
Copyright
Copyright © Cambridge Philosophical Society 1979

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References

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