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Article Dans Une Revue Physical Review E Année : 2022

Complete visitation statistics of one-dimensional random walks

Résumé

We develop a framework to determine the complete statistical behavior of a fundamental quantity in the theory of random walks, namely, the probability that n1,n2,n3,... distinct sites are visited at times t1,t2,t3,.... 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.

Dates et versions

hal-03735864 , version 1 (21-07-2022)

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Citer

Léo Régnier, Maxim Dolgushev, S. Redner, Olivier Bénichou. Complete visitation statistics of one-dimensional random walks. Physical Review E , 2022, 105 (6), pp.064104. ⟨10.1103/PhysRevE.105.064104⟩. ⟨hal-03735864⟩
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