Simulating a random walk with constant error

Joshua N. Cooper, Joel Spencer

Research output: Contribution to journalArticle

Abstract

We analyse Jim Propp's P-machine, a simple deterministic process that simulates a random walk on ℤ d to within a constant. The proof of the error bound relies on several estimates in the theory of simple random walks and some careful summing. We mention three intriguing conjectures concerning sign-changes and unimodality of functions in the linear span of {p(.,x): x ∈ ℤ d}where p(n, x) is the probability that a walk beginning from the origin arrives at x at time n.

Original languageEnglish (US)
Pages (from-to)815-822
Number of pages8
JournalCombinatorics Probability and Computing
Volume15
Issue number6
DOIs
StatePublished - Nov 2006

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Unimodality
Simple Random Walk
Sign Change
Walk
Error Bounds
Random walk
Estimate

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Mathematics(all)
  • Discrete Mathematics and Combinatorics
  • Statistics and Probability

Cite this

Simulating a random walk with constant error. / Cooper, Joshua N.; Spencer, Joel.

In: Combinatorics Probability and Computing, Vol. 15, No. 6, 11.2006, p. 815-822.

Research output: Contribution to journalArticle

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