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arXiv · 2501.17268

On the first positive position of a random walker

Claude Godrèche·Jean-Marc Luck
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Abstract

The distribution of the first positive position reached by a random walker starting from the origin is fundamental for understanding the statistics of extremes and records in one-dimensional random walks. We present a comprehensive study of this distribution, focusing particularly on its moments and asymptotic tail behaviour, in the case where the step distribution is continuous and symmetric, encompassing both diffusive random walks and L\'evy flights.

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Claude Godrèche, Jean-Marc Luck. 2025-01-28. On the first positive position of a random walker. https://doi.org/10.1007/s10955-025-03491-0

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