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Zbl 1056.15022
Kirkland, S.
Digraph-based conditioning for Markov chains. (English)
[J] Linear Algebra Appl. 385, 81-93 (2004). ISSN 0024-3795

For an irreducible stochastic matrix $T$, the author considers a certain condition number $c(T)$, which measures the stability of the corresponding stationary distribution when $T$ is perturbed, and then characterizes the strongly connected directed graphs $D$ such that $c(T)$ is bounded as $T$ ranges over $\Cal S_D$, the set of stochastic matrices whose directed graph is contained in $D$. For those digraphs $D$ for which $c(T)$ is bounded, the maximum value of $\{c(T)\mid T$ ranges over $\Cal S_D\}$ is determined.
[Huang Wenxue (Scarborough)]

MSC 2000:: *15A51 Stochastic matrices
15A18 Eigenvalues of matrices, etc.
60J10 Markov chains with discrete parameter
05C20 Directed graphs (digraphs)
15A12 Conditioning of matrices

Keywords: condition number; directed graph; Markov chain; stationary vector; stochastic matrix

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