Forward Jump Random Walk on a Cycle Graph and Its Hitting Time

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Published: Mar 29, 2024
Keywords:
Cycle graph Hitting time Random walk on graph

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Rachanai Kaikeaw
Faculty of Science and Technology, Dhonburi Rajabhat University, Bangkok 10600, Thailand
Pasin Marupanthorn
Department of Mathematics, Faculty of Science and Technology, Maejo University, Chiang Mai 50290, Thailand

Abstract

This paper presents an investigation into a random walk on a cycle graph with restricted forward movement at most 𝑚 steps, known as the forward jump random walk. The study derives exact formulas for the probability mass function of the arriving state, the hitting time, and its expected value and variance, where those solutions can be expressed in terms of trigonometric sums. These formulas are obtained using a combinatorial method as an alternative to the eigenvector-based approach commonly used.

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How to Cite
Rachanai Kaikeaw, & Pasin Marupanthorn. (2024). Forward Jump Random Walk on a Cycle Graph and Its Hitting Time. Science & Technology Asia, 29(1), 29–46. Retrieved from https://ph02.tci-thaijo.org/index.php/SciTechAsia/article/view/251338
Issue
Vol.29 No.1 (January-March 2024)
Section
Physical sciences
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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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