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Aug 27, 2016 at 14:38 comment added Nate Eldredge I guess maybe the relevance to probability is it illustrates that we cannot expect to obtain the LIL as an immediate consequence of SLLN and recurrence.
Aug 27, 2016 at 12:36 comment added Did "Nice construction that in addition to the comments above helped improving my understanding of random walks." The construction is allright but that it may help to advance the understanding of random walks is dubious since it is based on behaviours with zero probability. As already mentioned in the comments on main, this question is not related to probability (rather, to combinatorics).
Aug 26, 2016 at 1:27 comment added Nate Eldredge Variants of this can give you walks whose asymptotic growth rate is anything smaller than $n$. Here I just chose $n^{2/3}$ but if you want $n/\log n$ or $n/\log\log\log\log n$ that would work just as well.
Aug 25, 2016 at 22:31 comment added user45947 Nice construction that in addition to the comments above helped improving my understanding of random walks. Thanks!
Aug 25, 2016 at 22:28 vote accept user45947
Aug 25, 2016 at 14:13 history answered Nate Eldredge CC BY-SA 3.0