Phase transitions for a unidirectional elephant random walk with a power law memory

Rahul Roy; Masato Takei; Hideki Tanemura

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arXiv · 2402.02048

Phase transitions for a unidirectional elephant random walk with a power law memory

Rahul Roy·Masato Takei·Hideki Tanemura

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Abstract

For the standard elephant random walk, Laulin (2022) studied the case when the increment of the random walk is not uniformly distributed over the past history instead has a power law distribution. We study such a problem for the unidirectional elephant random walk introduced by Harbola, Kumar and Lindenberg (2014). Depending on the memory parameter $p$ and the power law exponent $\beta$, we obtain three distinct phases in one such phase the elephant travels only a finite distance almost surely, and the other two phases are distinguished by the speed at which the elephant travels.

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Rahul Roy, Masato Takei, Hideki Tanemura. 2024-02-03. Phase transitions for a unidirectional elephant random walk with a power law memory. https://arxiv.org/abs/2402.02048

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