Transition from Kardar-Parisi-Zhang to tilted interface critical behavior in a solvable asymmetric avalanche model

We use a discrete-time formulation of the asymmetric avalanche process (ASAP) [Phys. Rev. Lett. 87, 084301 (2001)]] of p particles on a finite ring of N sites to obtain an exact expression for the average avalanche size as a function of toppling probabilities and particle density rho=p/N. By mapping the model onto driven interface problems, we find that the ASAP incorporates the annealed Kardar-Parizi-Zhang and quenched tilted interface dynamics for rhorho(c), respectively, with rho(c) being the critical density for given toppling probabilities and N--> infinity. We analyze the crossover between two regimes and show which parameters are relevant near the transition point.