Date of this Version
Journal of Computational and Applied Mathematics
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.
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Spitzer's combinatorial lemma, random walk, convex hull, permutations, cycle decomposition, cycle lemma
Steele, J. M. (2002). The Bohnenblust–Spitzer Algorithm and its Applications. Journal of Computational and Applied Mathematics, 142 (1), 235-249. http://dx.doi.org/10.1016/S0377-0427(01)00472-1
Date Posted: 27 November 2017
This document has been peer reviewed.