Simulating a Random Walk with Constant Error
Abstract
We analyze Jim Propp's Pmachine, 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 signchanges and unimodality of functions in the linear span of $\{p(\cdot,x) : x \in Z^d\}$, where $p(n,x)$ is the probability that a walk beginning from the origin arrives at $x$ at time $n$.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 2004
 arXiv:
 arXiv:math/0402323
 Bibcode:
 2004math......2323C
 Keywords:

 Combinatorics;
 Probability;
 82B41;
 60G50
 EPrint:
 8 Pages, 0 Figures