New insights into the distribution of the topmost gap in random walks and Lévy flights

2025/02/25 by Godrèche, Claude, Luck, Jean-Marc · 1 citation
#FOS: Mathematics #FOS: Physical sciences #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2502.18391

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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• The first positive position of a lattice random walk

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