Operations, Information and Decisions Papers

Document Type

Journal Article

Date of this Version

5-2002

Publication Source

Journal of Computational and Applied Mathematics

Volume

142

Issue

1

Start Page

235

Last Page

249

DOI

10.1016/S0377-0427(01)00472-1

Abstract

The familiar bijections between the representations of permutations as words and as products of cycles have a natural class of “data driven” extensions that permit us to use purely combinatorial means to obtain precise probabilistic information about the geometry of random walks. In particular, we show that the algorithmic bijection of Bohnenblust and Spitzer can be used to obtain means, variances, and concentration inequalities for several random variables associated with a random walk including the number of vertices and length of the convex minorant, concave majorant, and convex hull.

Copyright/Permission Statement

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

Spitzer's combinatorial lemma, random walk, convex hull, permutations, cycle decomposition, cycle lemma

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Date Posted: 27 November 2017

This document has been peer reviewed.