Skip to main content
Article thumbnail
Location of Repository

Random walks whose concave majorants often have few faces

By Zhihua Qiao and J. Michael Steele

Abstract

We construct a continuous distribution G such that the number of faces in the smallest concave majorant of the random walk with G-distributed summands will take on each natural number infinitely often with probability one. This investigation is motivated by the fact that the number of faces Fn of the concave majorant of the random walk at time n has the same distribution as the number of records Rn in the sequence of summands up to time n. Since Rn is almost surely asymptotic to , the construction shows that despite the equality of all of the one-dimensional marginals, the almost sure behaviors of the sequences {Rn} and {Fn} may be radically different.Spitzer's combinatorial lemma Random walk Convex hull Convex minorant Concave majorant

OAI identifier:
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://www.sciencedirect.com/s... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.