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By considering a random walk with jumps with steps ( \(+3\) ) or ( \(-1\) ), 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.

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

  • 章节

  • 发表日期：

    2025年

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  • Chrysoula Ganatsiou,
  • Ilias K. Savvas,
  • Apostolos Xenakis

摘要

By considering a random walk with jumps with steps ( \(+3\) ) or ( \(-1\) ), 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.