The paper establishes the lower bound for the downward-deviation probability of the maximum local time of discrete-time simple random walks in d ≥ 3 via a new loop-pruned random walk structure, yielding the sharp asymptotic.
Some problems concerning the structure of random walk paths
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Loop pruning and downward deviations for maximum local time of discrete-time simple random walks
The paper establishes the lower bound for the downward-deviation probability of the maximum local time of discrete-time simple random walks in d ≥ 3 via a new loop-pruned random walk structure, yielding the sharp asymptotic.