Geodesic
Completion problems and sparsity for Kemeny’s constant
Canadian mathematical bulletin, Tome 68 (2025) no. 1, pp. 1-18

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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.
DOI : 10.4153/S0008439524000419
Mots-clés : Kemeny’s constant, stochastic matrix, matrix completion 
Kirkland, Steve. Completion problems and sparsity for Kemeny’s constant. Canadian mathematical bulletin, Tome 68 (2025) no. 1, pp. 1-18. doi: 10.4153/S0008439524000419
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