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

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...

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Bibliographic Details
Published in:arXiv.org 2014-02
Main Authors: Foldes, Antonia, Revesz, Pal
Format: Article
Language:English
Subjects:
Legs
Random walk
Random walk theory
Online Access:Get full text
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Summary: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.
ISSN:2331-8422