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 $\mathbb{Z}$, 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 restart mechanisms such as sharp, Poisson and Zeta distribution where the latter is heavy tailed. We emphasize that the method is very useful to treat such problems both analytically and numerically.

8 pages. Short note. arXiv admin note: text overlap with arXiv:2102.00895

References in corpus (3)

• First Passage Under Restart
• First order transition for the optimal search time of Lévy flights with resetting
• First Passage with Restart in Discrete Time: with applications to biased random walks on the half-line

Cited by in corpus (1)

• First Passage with Restart in Discrete Time: with applications to biased random walks on the half-line