Temperley-Lieb Stochastic Processes
  We discuss one-dimensional stochastic processes defined through the Temperley-Lieb algebra related to the Q=1 Potts model. For various boundary conditions, we formulate a conjecture relating the probability distribution which describes the stationary state, to the enumeration of a symmetry class of alternating sign matrices, objects that have received much attention in combinatorics. 
Paul A. Pearce, Vladimir Rittenberg, Jan de Gier and Bernard Nienhuis