Journal
PHYSICAL REVIEW E
Volume 105, Issue 6, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.105.064104
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Funding
- NSF [DMR-1910736]
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We develop a framework to determine the statistical behavior of the probability of visiting distinct sites at different times in the theory of random walks. We show that the visitation statistics of one-dimensional random walks are temporally correlated and quantify the non-Markovian nature of the process. We apply these ideas to the two-time trapping problem and the visitation statistics of run-and-tumble particle and biased random walk.
We develop a framework to determine the complete statistical behavior of a fundamental quantity in the theory of random walks, namely, the probability that n(1), n(2), n(3), ... distinct sites are visited at times t(1), t(2), t(3),... From this multiple-time distribution, we show that the visitation statistics of one-dimensional random walks are temporally correlated, and we quantify the non-Markovian nature of the process. We exploit these ideas to derive unexpected results for the two-time trapping problem and to determine the visitation statistics of two important stochastic processes, the run-and-tumble particle and the biased random walk.
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