Polytopes of Stochastic Tensors
Annals of Functional Analysis
Doubly stochastic matrix, Extreme point, Polytope, Stochastic semi-magic cube, Stochastic tensor
Considering n × n × n stochastic tensors (aijk)(i.e., nonnegative hypermatrices in which every sum over one index i, j, or k, is 1), we study the polytope (Ωn) of all these tensors, the convex set (Ln) of all tensors in Ωn with some positive diagonals, and the polytope (Δn) generated by the permutation tensors. We show that LnLn is almost the same as Ωn except for some boundary points. We also present an upper bound for the number of vertices of Ωn.
Chang, Haixia; Paksoy, Vehbi Emrah; and Zhang, Fuzhen, "Polytopes of Stochastic Tensors" (2016). Mathematics Faculty Articles. 205.