English

Completion Problems and Sparsity for Kemeny's Constant

Spectral Theory 2023-08-22 v1 Probability

Abstract

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.

Keywords

Cite

@article{arxiv.2308.10259,
  title  = {Completion Problems and Sparsity for Kemeny's Constant},
  author = {Stephen Kirkland},
  journal= {arXiv preprint arXiv:2308.10259},
  year   = {2023}
}
R2 v1 2026-06-28T11:59:45.829Z