Gingell, K. (2021). A characterization of the set of invariant distributions of a random walk on a graph. https://scholar.acadiau.ca/islandora/object/theses:3589

A characterization of the set of invariant distributions of a random walk on a graph

Author

Gingell, Kate

Call Number

LE3 .A278 2021

Date

2021

Supervisor

Mendivil, Franklin

Degree Grantor

Acadia University

Degree Name

Bachelor of Science

Degree Level

Honours

Discipline

Mathematics and Statistics

Affiliation

Mathematics & Statistics

Abstract

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.

Rights

The author grants permission to the University Librarian at Acadia University to reproduce, loan or distribute copies of my thesis in microform, paper or electronic formats on a non-profit basis. The author retains the copyright of the thesis.