On the Study of Cycle Chains Representing Non-reversible Markov Chains Associated with Random Walks with Jumps in Fixed Environments

Chrysoula Ganatsiou (), Ilias K. Savvas () and Apostolos Xenakis ()
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Chrysoula Ganatsiou: University of Thessaly
Ilias K. Savvas: University of Thessaly
Apostolos Xenakis: University of Thessaly

A chapter in Optimization, Discrete Mathematics and Applications to Data Sciences, 2025, pp 91-103 from Springer

Abstract: Abstract By considering a random walk with jumps with steps ( + 3 $$+3$$ ) or ( −1 $$-1$$ ), we investigate the unique representations by cycles and weights of the corresponding non-reversible Markov chains (cycle chains) describing the abovementioned random walk in fixed environments. This will give us the possibility to find a suitable criterion regarding the properties of recurrence and transience of the abovementioned cycle chains in fixed environments.

Date: 2025
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DOI: 10.1007/978-3-031-78369-2_6

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