2021
DOI: 10.48550/arxiv.2106.14036
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The Pólya and Sisyphus lattice random walks with resetting -- a first passage under restart approach

Abstract: We revisit the simple lattice random walk (Pólya walk) and the Sisyphus random walk in Z, in the presence of random restarts. We use a relatively direct approach namely First passage under restart for discrete space and time which was recently developed by us in PRE 103, 052129 (2021) and rederive the first passage properties of these walks under the memoryless geometric restart mechanism. Subsequently, we show how our method could be generalized to arbitrary first passage process subject to more complex resta… Show more

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Cited by 2 publications
(3 citation statements)
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“…The criterion for the underlying process (γ = 0) in this case reads z 2 i j (0) > 1 − 1/ T i j (0) [57]. In a subsequent study [58], the same authors have taken into consideration the duration of a resetting event in the renewal equations, obtaining the same criteria (36).…”
Section: Two General Conditions For the First Passage Time Fluctuationsmentioning
confidence: 99%
See 1 more Smart Citation
“…The criterion for the underlying process (γ = 0) in this case reads z 2 i j (0) > 1 − 1/ T i j (0) [57]. In a subsequent study [58], the same authors have taken into consideration the duration of a resetting event in the renewal equations, obtaining the same criteria (36).…”
Section: Two General Conditions For the First Passage Time Fluctuationsmentioning
confidence: 99%
“…The study of discrete-time processes under the influence of resetting is relatively recent. Several results have been derived in those cases, mostly on the line or one-dimensional lattices [47][48][49][50][51][52][53][54][55][56][57][58]. Reference [47] provides a general formula that relates the survival probability of a generic discrete-time process subject to geometric resetting to the one without resetting.…”
Section: Introductionmentioning
confidence: 99%
“…Thus, all the observables of our interest are computable from solutions (6) by straightforward calculations, according to formulae (7) or (8) for W 0 , W N , (11)-for t 0 , t N , and ( 14), or (10), or (12)-for t . True, for further analytical conclusions (like, for example, 'benefit criterion' in [35]) the expressions ( 5) and ( 6) are less convenient than those in particular cases of the continuous models and become too cumbersome for N > 2 (cf [10]).…”
Section: Observables To Calculatementioning
confidence: 99%