arXiv subjects

Timothy Prescott

Publications and source records attributed to Timothy Prescott.

2 recordsLinked to original sources

arXiv2004

Random walks on the torus with several generators

Our paper gives bounds for the rate of convergence for a class of random walks on the d-dimensional torus generated by a set of n vectors in R^d/Z^d. We give bounds on the discrepancy distance from Haar measure; our lower bound holds for all such walks, and if the generators arise from the rows of a "badly approximable" matrix, then there is a corresponding upper bound. The bounds are sharp for walks on the circle.

math.PR↗

arXiv2003

A Constructive Proof of Ky Fan's Generalization of Tucker's Lemma

We present a constructive proof of Ky Fan's combinatorial lemma concerning labellings of triangulated spheres. Our construction works for triangulations of $S^n$ that contain a flag of hemispheres. As a consequence, we produce a constructive proof of Tucker's lemma that holds for a larger class of triangulations than previous constructive proofs.

math.CO↗