Density profiles in the raise and peel model with and without a wall. Physics and combinatorics
Journal of Statistical Mechanics: Theory and Experiment. 2008. Vol. P01006. P. 1-38.
We consider the raise and peel model of a one-dimensional fluctuating interface in the presence of an attractive wall. The model can also describe a pair annihilation process in a disordered unquenched media with a source at one end of the system. For the stationary states, several density profiles are studied usingMonte Carlo simulations. We point out a deep connection between some profiles seen in the presence of the wall and in 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 obtained using combinatorial methods. We have solved known (Pascal’s hexagon)and new (split-hexagon) bilinear recurrence relations. The solutions of these equations are interesting on their own since they give information on certain classes of alternating sign matrices.