Stationary vectors of stochastic matrices subject to combinatorial constraints
نویسندگان
چکیده
Given a strongly connected directed graph D, let SD denote the set of all stochastic matrices whose directed graph is a spanning subgraph of D. We consider the problem of completely describing the set of stationary vectors of irreducible members of SD . Results from the area of convex polytopes and an association of each matrix with an undirected bipartite graph are used to derive conditions which must be satisfied by a positive probability vector x in order for it to be admissible as a stationary vector of some matrix in SD . Given some admissible vector x, the set of matrices in SD that possess x as a stationary vector is also characterised. This paper is dedicated to the memory of David Gregory.
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تاریخ انتشار 2017