Random walk in a Weyl chamber

Abstract

The classical Ballot problem that counts the number of ways of walking from the origin and staying within the wedge x 1 ≥ x 2 ≥ ⋯ ≥ x n {x_1} \geq {x_2} \geq \cdots \geq {x_n} (which is a Weyl chamber for the symmetric group), using positive unit steps, is generalized to general Weyl groups and general sets of steps.