"Lengths and heights of random walk excursions"

Endre Csáki and Yueyun Hu

Summary: 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 for Brownian motion.

Keywords: Simple ramdom walk, excursion length, excursion height.

AMS 2000 subject classification: 60G50 60F05.