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

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.

22 pages, 4 figures

References in corpus (2)

• On the Gap and Time Interval between the First Two Maxima of Long Random Walks
• On the first positive position of a random walker