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math.PR2025
Capacity of the range of random walk: Moderate deviations in dimensions 4 and 5
Arka Adhikari, Jiyun Park
We prove a moderate deviation principle for the capacity of the range of random walk in . Depending on the scale of deviation, we get two different regimes. We observ…
math.PR2024
Upper tails of subgraph counts in directed random graphs
Jiyun Park
The upper tail problem in a sparse Erdős-Rényi graph asks for the probability that the number of copies of some fixed subgraph exceeds its expected value by a constant factor. We s…