A characterization of the set of invariant distributions of a random walk on a graph
LE3 .A278 2021
Bachelor of Science
Mathematics and Statistics
Mathematics & Statistics
In this paper, a characterization of the set of attainable limiting distributions of a random walk on a strongly connected directed graph is described. This result is shown in terms of the invariant distributions of Markov chains. The exisitence of invariant distributions of Markov chains is proven by way of the Perron-Frobenius theorem. Then it is shown that the set of possible limiting distributions of a graph Gis the convex hull of the uniform cycle distributions of the cycles of G.
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