DMTCS Proceedings, Discrete Random Walks, DRW'03

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DMTCS Conference vol AC (2003), pp. 45-52


Discrete Random Walks, DRW'03

Cyril Banderier and Christian Krattenthaler (eds.)

DMTCS Conference Volume AC (2003), pp. 45-52

author: Endre Csáki and Yueyun Hu
title: Lengths and heights of random walk excursions
keywords: simple random walk, excursion length, excursion height
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.
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reference: Endre Csáki and Yueyun Hu (2003), Lengths and heights of random walk excursions, in Discrete Random Walks, DRW'03, Cyril Banderier and Christian Krattenthaler (eds.), Discrete Mathematics and Theoretical Computer Science Proceedings AC, pp. 45-52
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