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arXiv · 2502.18391

New insights into the distribution of the topmost gap in random walks and L\'evy flights

Claude Godrèche·Jean-Marc Luck
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Abstract

Building upon the knowledge of the distribution of the first positive position reached by a random walker starting from the origin, one can derive new results on the statistics of the gap between the largest and second-largest positions of the walk, and recover known ones in a more direct manner.

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Claude Godrèche, Jean-Marc Luck. 2025-02-25. New insights into the distribution of the topmost gap in random walks and L\'evy flights. https://doi.org/10.1088/1742-5468%2Fadec65

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