Csáki, Endre and Hu, Yueyun - Lengths and heights of random walk excursions

dmtcs:3337 - Discrete Mathematics & Theoretical Computer Science, January 1, 2003, DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03)
Lengths and heights of random walk excursions

Authors: Csáki, Endre and Hu, Yueyun

Consider a simple symmetric random walk on the line. The parts of the random walk between consecutive returns to the origin are called excursions. The heights and lengths of these excursions can be arranged in decreasing order. In this paper we give the exact and limiting distributions of these ranked quantities. These results are analogues of the corresponding results of Pitman and Yor [1997, 1998, 2001] for Brownian motion.


Volume: DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03)
Section: Proceedings
Published on: January 1, 2003
Submitted on: May 10, 2017
Keywords: simple random walk,excursion length,excursion height,[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG]


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