English

Stationary probability vectors of higher-order two-dimensional transition probability tensors

Spectral Theory 2018-03-01 v1

Abstract

In this paper we investigate stationary probability vectors of higher-order two-dimensional symmetric transition probability tensors. We show that there are two special symmetric transition probability tensors of order mm dimension 2, which have and only have two stationary probability vectors; and any other symmetric transition probability tensor of order mm dimension 2 has a unique stationary probability vector. As a byproduct, we obtain that any symmetric transition probability tensor of order mm dimension 2 has a unique positive stationary probability vector; and that any symmetric irreducible transition probability tensor of order mm dimension 2 has a unique stationary probability vector.

Keywords

Cite

@article{arxiv.1802.10270,
  title  = {Stationary probability vectors of higher-order two-dimensional transition probability tensors},
  author = {Zheng-Hai Huang and Liqun Qi},
  journal= {arXiv preprint arXiv:1802.10270},
  year   = {2018}
}