I am trying to do a research project for school on markov chains and Diophantine equations. I need to cite the significance of the study and the only place I can find any connection between the 2 is the markov equation. I have spent hours trying to find the purpose of the markov equation with no success.
2026-05-14 12:35:54.1778762154
What is the purpose of the Markov equation?
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See [1], [2] for applications of Diophantine approximation to Markov chains.
[1] Angel, Omer, Yuval Peres, and David B. Wilson. "Card shuffling and Diophantine approximation." The Annals of Applied Probability 18, no. 3 (2008): 1215-1231. https://projecteuclid.org/journals/annals-of-applied-probability/volume-18/issue-3/Card-shuffling-and-Diophantine-approximation/10.1214/07-AAP484.short
[2] Boczkowski, L., Peres, Y., & Sousi, P. (2018). Sensitivity of mixing times in Eulerian digraphs. SIAM Journal on Discrete Mathematics, 32(1), 624-655. https://epubs.siam.org/doi/abs/10.1137/16M1073376