Simulating a Random Walk with Constant Error

@misc{citeulike:2967852, abstract = {We analyze 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(\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\$.}, author = {Cooper, Joshua N. and Spencer, Joel }, citeulike-article-id = {2967852}, eprint = {math/0402323}, keywords = {deterministic, probability-course, random-walk}, month = {Apr}, posted-at = {2008-07-06 21:20:26}, priority = {2}, title = {Simulating a Random Walk with Constant Error}, url = {http://arxiv.org/abs/math/0402323}, year = {2004} }

TY - ELEC ID - citeulike:2967852 L3 - citeulike-article-id:2967852 TI - Simulating a Random Walk with Constant Error N2 - We analyze 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 $\{p(\cdot,x) : x \in Z^d\}$, where $p(n,x)$ is the probability that a walk beginning from the origin arrives at $x$ at time $n$. KW - deterministic KW - probability-course KW - random-walk AU - Cooper, Joshua AU - Spencer, Joel PY - 2004/Apr/12/ UR - http://arxiv.org/abs/math/0402323 ER -