The appearance of numbers enumerating alternating sign matrices in stationary
states of certain stochastic processes is reviewed. New conjectures concerning
nest distribution functions are presented as well as a bijection between
certain classes of alternating sign matrices and lozenge tilings of hexagons
with cut off corners.Comment: LaTeX, 26 pages, 44 figures, extended version of a talk given at the
14th International Conference on Formal Power Series and Algebraic
Combinatorics (Melbourne 2002); Version2: Changed title, expanded some
sections and included more picture