Large deviations of avalanches in the raise and peel model
We study the large deviation functions for two quantities characterizing the avalanche dynamics in the Raise and Peel model: the number of tiles removed by avalanches and the number of global avalanches extending through the whole system. To this end, we exploit their connection to the groundstate eigenvalue of the XXZ model with twisted boundary conditions. We evaluate the cumulants of the two quantities asymptotically in the limit of the large system size. The first cumulants, the means, confirm the exact formulas conjectured from analysis of finite systems. We discuss the phase transition from critical to non-critical behaviour in the rate function of the global avalanches conditioned to an atypical values of the number of tiles removed by avalanches per unit time.