Laws of large numbers in the raise and peel model

Abstract

We establish the exact laws of large numbers for two time additive quantities in the raise and peel model, the number of tiles removed by avalanches and the number of global avalanches happened by given time. The validity of conjectures for the related stationary state correlation functions then follow. The proof is based on the technique of Baxter’s T-Q equation applied to the associated XXZ chain and on its solution at obtained by Fridkin, Stroganov and Zagier.