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

Antonia Foldes; Pal Revesz

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arXiv · 1402.5682

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

Antonia Foldes·Pal Revesz

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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.

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Antonia Foldes, Pal Revesz. 2014-02-23. How Tall Can Be the Excursions of a Random Walk on a Spider. https://arxiv.org/abs/1402.5682

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