"Long excursions of a random walk"

Endre Csáki, Pál Révész and Zhan Shi

Summary: In Csáki, Révész and Rosen (1998) and Révész and Willekens (1988), it was proved that the length of the longest excursion among the first n excursions of a plane random walk is nearly equal to the total sum of the lengths of these excursions. In this paper several results are proved in the same spirit, for plane random walks and for random walks in higher dimensions.

Keywords: Random walk, excursion length.

AMS 1991 subject classification: 60J15.