Abstract
We consider the raise and peel model of a one-dimensional fluctuating interface in thepresence of an attractive wall. The model can also describe a pair annihilation process indisordered unquenched media with a source at one end of the system. For the stationarystates, several density profiles are studied using Monte Carlo simulations. We point outa deep connection between some profiles seen in the presence of the wall andin its absence. Our results are discussed in the context of conformal invariance(c = 0 theory). We discover some unexpected values for the critical exponents, which are obtainedusing combinatorial methods. We have solved known (Pascal’s hexagon) and new(split-hexagon) bilinear recurrence relations. The solutions of these equations areinteresting in their own right since they give information on certain classes of alternatingsign matrices.
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