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Discrete Mathematics & Theoretical Computer Science |
3337
Endre Csáki ; Yueyun Hu - 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) - https://doi.org/10.46298/dmtcs.3337Lengths and heights of random walk excursions
- 1 Alfréd Rényi Institute of Mathematics
- 2 Laboratoire de Probabilités et Modèles Aléatoires
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.
Source: HAL:hal-01183932v1
Volume: DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03)
Section: Proceedings
Published on: January 1, 2003
Imported 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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IsRelatedTo ARXIV 1706.05621 Source : ScholeXplorer IsRelatedTo DOI 10.1093/imrn/rnaa166 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1706.05621
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