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.
Large deviations for maximum local time of simple random walk in dimensions $d\ge 3$
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abstract
We obtain sharp asymptotic probabilities for upward and downward large deviations of the maximum local time of simple random walks on $\mathbb{Z}^d$, $d \ge 3$. We also obtain Gumbel-type fluctuations around the logarithmic scale of the maximum local time.
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2026 1verdicts
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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.