Completion problems and sparsity for Kemeny’s constant

For a partially specified stochastic matrix, we consider the problem of completing it so as to minimize Kemeny’s constant. We prove that for any partially specified stochastic matrix for which the problem is well defined, there is a minimizing completion that is as sparse as possible. We also find t...

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Bibliographic Details
Published inCanadian mathematical bulletin Vol. 68; no. 1; pp. 1 - 18
Main Author Kirkland, Steve
Format Journal Article
LanguageEnglish
Published Canada Canadian Mathematical Society 01.03.2025
Subjects
60J10
stochastic matrix
15B51
15A83
matrix completion
Kemeny’s constant
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Summary:For a partially specified stochastic matrix, we consider the problem of completing it so as to minimize Kemeny’s constant. We prove that for any partially specified stochastic matrix for which the problem is well defined, there is a minimizing completion that is as sparse as possible. We also find the minimum value of Kemeny’s constant in two special cases: when the diagonal has been specified and when all specified entries lie in a common row.
ISSN:0008-4395
1496-4287
DOI:10.4153/S0008439524000419