4 papers
Random Walk in an Alcove of an Affine Weyl Group, and Non-Colliding Random Walks on an Interval
David J. Grabiner
We use a reflection argument, introduced by Gessel and Zeilberger, to count the number of k-step walks between two points which stay within a chamber of a Weyl group. We apply this…
Brownian Motion in a Weyl Chamber, Non-Colliding Particles, and Random Matrices
David J. Grabiner
Let particles move in standard Brownian motion in one dimension, with the process terminating if two particles collide. This is a specific case of Brownian motion constrained t…
Cutting Sequences for Geodesic Flow on the Modular Surface and Continued Fractions
David J. Grabiner, Jeffrey C. Lagarias
This paper describes the cutting sequences of geodesic flow on the modular surface H/PSL(2,Z) with respect to the standard fundamental domain F = {z=x+iy: -1/2 <= x <= 1/2 and |z|>…
Continued Fractions and Unique Additive Partitions
David J. Grabiner
A partition of the positive integers into sets and {\em avoids} a set if no two distinct elements in the same part have a sum in . If the partition is uniqu…