Publication Date
12-2025
Date of Final Oral Examination (Defense)
10-23-2025
Type of Culminating Activity
Thesis
Degree Title
Master of Science in Mathematics
Department
Mathematics
Supervisory Committee Chair
Zachariah Teitler, Ph.D.
Supervisory Committee Member
Jens Harlander, Ph.D.
Supervisory Committee Member
John Clemens, Ph.D.
Abstract
The abelian sandpile model is a Markov chain that is able to decompose any recurrent configuration into a basic alive divisor, some amount of sand placed on the sink vertex, and a series of vertex firings. In this paper we begin to explore some of the dynamics of this system when the edges of the graph are allowed to alternate between two different edge sets. This system will be framed in a similar fashion as the classical model, and then some basic numerical simulations were used to observe the threshold behavior of the system. We lay some of the initial groundwork and identify several areas for expanding upon this work.
DOI
https://doi.org/10.18122/td.2462.boisestate
Recommended Citation
Lyons, Payton, "Abelian Sandpile Models on Edge Periodic Graphs" (2025). Boise State University Theses and Dissertations. 2462.
https://doi.org/10.18122/td.2462.boisestate