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原文連結
論文資訊
- 類型：已發表論文
- 日期：2022-10-01
摘要
The set of visited sites and the number of visited sites are two basic properties of the random walk trajectory. We consider two independent random walks on hyper-cubic lattices and study ordering probabilities associated with these characteristics. The first is the probability that during the time interval (0, t), the number of sites visited by a walker never exceeds that of another walker. The second is the probability that the sites visited by a walker remain a subset of the sites visited by another walker. Using numerical simulations, we investigate the leading asymptotic behaviors of the ordering probabilities in spatial dimensions d = 1, 2, 3, 4. We also study the time 演化 of the number of ties between the number of visited sites. We show analytically that the average number of ties i
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