Kirkland, Steve (2009) Subdominant Eigenvalues for Stochastic Matrices with Given Column Sums. Electronic Journal of Linear Algebra, 18. pp. 784800. ISSN 10813810
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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 rowstochastic 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 
URI:  
Use Licence:  This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BYNCSA). Details of this licence are available here 
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