Random Walks on Graphs
Alex Rimkevicus
A research project investigating three properties of random walks on networks.
Suppose you were tracking the movement of animals in a forest, or the Brownian motion of a particle. How long would it take the animal or the molecule to get from point A to point B? What about getting from Point A to Point B and back? How long would it take for it to reach every point on the network? These are some of the questions this investigation seeks to answer.
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This project focusses on a mathematical analysis of random walks on graphs and three properties resulting from them: hitting time, commute time and cover time. This project’s final results are composed of mathematical formulae describing these quantities as well as PDF and CDFs of these values in the general case. Additionally, execution and simulation in MATLAB were used to verify findings.
