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This research focuses on extending the definition of maximal entropy random walks and establishing rigorous foundational tools for infinite graphs.

Maximum Entropy Random Walks: the Infinite Setting and the Example of Spider Networks with their Scaling Limits

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This research focuses on extending the definition of maximal entropy random walks and establishing rigorous foundational tools for infinite graphs.
Introduced a generalized definition of maximal entropy random walks.
Performed an in-depth analysis of weighted spider networks.
Provided a unified proof of scaling limits using submartingale problems.
Identified significant computational challenges in maximizing global entropy.
Revealed phenomena characteristic of infinite graphs, including phase transitions.
Demonstrated the continuity of entropy maximization even in infinite settings.

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This work demonstrates phase transitions in random walks on infinite graphs, indicating complexities in scaling limits and entropy maximization.

Duboux et al. (2026) studied this question.

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This work demonstrates phase transitions in random walks on infinite graphs, indicating complexities in scaling limits and entropy maximization.