Geodesic
Subdominant eigenvalues for stochastic matrices with given column sums
The electronic journal of linear algebra, Tome 18 (2009), pp. 784-800.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: For any stochastic matrix A of order n, denote its eigenvalues as $\lambda 1$ ( A), . . . , $\lambda n$ ( A), ordered so that 1 = |$\lambda 1$ ( A)$| \geq |\lambda 2$ ( A)| $\geq . . . \geq |\lambda n$ ( A)|. Let c Tbe a row vector of order n whose entries are nonnegative numbers that sum to n. Define $S(c)$, to be the set of n $\times n$ row-stochastic matrices with column sum vector c T. In this paper the quantity $\lambda (c) = $max|$\lambda 2$ ( A)||A $\in S(c)$ is considered. The vectors c Tsuch that $\lambda (c)$ 1 are identified and in those cases, nontrivial upper bounds on $\lambda (c)$ and weak ergodicity results for forward products are provided. The results are obtained via a mix of analytic and combinatorial techniques.
Classification : 15A51, 15A18, 15A42, 60J10
Keywords: stochastic matrix, subdominant eigenvalue, bipartite graph 
@article{ELA_2009__18__a1,
     author = {Kirkland, Stephen J.},
     title = {Subdominant eigenvalues for stochastic matrices with given column sums},
     journal = {The electronic journal of linear algebra},
     pages = {784--800},
     publisher = {mathdoc},
     volume = {18},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2009__18__a1/}
}
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Kirkland, Stephen J. Subdominant eigenvalues for stochastic matrices with given column sums. The electronic journal of linear algebra, Tome 18 (2009), pp. 784-800. http://geodesic.mathdoc.fr/item/ELA_2009__18__a1/