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  1. Home > Articles & Issues >
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  3. Lengths and heights ...
Conference paper

Lengths and heights of random walk excursions

Endre Csáki (1), Yueyun Hu (2)
(1) Alfréd Rényi Institute of Mathematics
(2) Laboratoire de Probabilités et Modèles Aléatoires
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Imported on
May 10, 2017
Published on
December 31, 2002
Last modified on
March 31, 2025
Volume 0
DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03)
Proceedings
DOI
10.46298/dmtcs.3337
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https://about.hal.science/hal-authorisation-v1
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Lengths and heights of random walk excursions

Endre Csáki (1), Yueyun Hu (2)
(1) Alfréd Rényi Institute of Mathematics
(2) Laboratoire de Probabilités et Modèles Aléatoires
Abstract
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.
Keywords
  • [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]
  • simple random walk
  • excursion length
  • excursion height
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