Return of $k$-bonacci random walks

Najmeddine Attia; Chouhaïd Souissi

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arXiv · 1911.11708

Return of $k$-bonacci random walks

Najmeddine Attia·Chouhaïd Souissi

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Abstract

In this work, the probability of return for random walks on $\mathbb{Z}$, whose increment is given by the $k$-bonacci sequence, is determined. Also, the Hausorff, packing and box-counting dimensions of the set of these walks that return an infinite number of times to the origin are given. As an application, we study the return for tribonacci random walks to the first term of the tribonacci sequence.

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Najmeddine Attia, Chouhaïd Souissi. 2019-11-23. Return of $k$-bonacci random walks. https://arxiv.org/abs/1911.11708

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