Recurrence and transience criteria for nonadaptive random walks in changing environments

A nonadaptive random walk in changing environment (nonadaptive RWCE) is a random walk whose edge weights are chosen in advance and therefore do not depend on the walker's location. For the four criteria referred to in the source as Theorems

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,

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, generalization conjecture. These theorems remain true for nonadaptive RWCE on any graph. The conjecture proposes that the recurrence and transience criteria established earlier extend from the original setting to arbitrary graphs; the referenced theorem statements are not included in the supplied text, so their precise hypotheses and conclusions cannot be reproduced here.