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Kirkland, Steve (2009) Subdominant Eigenvalues for Stochastic Matrices with Given Column Sums. Electronic Journal of Linear Algebra, 18. pp. 784-800. ISSN 1081-3810
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Abstract
For any stochastic matrix A of order n, denote its eigenvalues as λ1(A), . . . ,λn(A), ordered so that 1 = |λ1(A)| ≥ |λ2(A)| ≥ . . . ≥ |λn(A)|. Let cT be a row vector of order n whose entries are nonnegative numbers that sum to n. Define S(c), to be the set of n × n row-stochastic
matrices with column sum vector cT . In this paper the quantity λ(c) = max{|λ2(A)||A ∈ S(c)} is considered. The vectors cT such that λ(c) < 1 are identified and in those cases, nontrivial upper bounds on λ(c) and weak ergodicity results for forward products are provided. The results are
obtained via a mix of analytic and combinatorial techniques.
| Item Type: | Article |
|---|---|
| Keywords: | Stochastic matrix; Subdominant eigenvalue; Bipartite graph; Hamilton Institute. |
| Academic Unit: | Faculty of Science and Engineering > Research Institutes > Hamilton Institute Faculty of Science and Engineering > Mathematics and Statistics |
| Item ID: | 1896 |
| Depositing User: | Hamilton Editor |
| Date Deposited: | 24 Mar 2010 16:20 |
| Journal or Publication Title: | Electronic Journal of Linear Algebra |
| Publisher: | ILAS - International Linear Algebra Society |
| Refereed: | Yes |
| Related URLs: | |
| URI: | https://mural.maynoothuniversity.ie/id/eprint/1896 |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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