How Tall Can Be the Excursions of a Random Walk on a Spider

Publication date: 23 February 2014

Abstract: We consider a simple symmetric random walk on a spider, that is a collection of half lines (we call them legs) joined at the origin. Our main question is the following: if the walker makes

n

steps how high can he go up on all legs. This problem is discussed in two different situations; when the number of legs are increasing, as

n

goes to infinity and when it is fixed.

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15) Brownian motion (60J65) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10)

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