Finite size behavior of the asymmetric avalanche process

We study the behavior of particle flow in the asymmetric avalanche process with partially asymmetric diffusion below the line separating phases of intermittent and continuous flow. Besides the average velocity of flow, that can be obtained in the limit of infinite system size, we obtain the other quantities, such as the dispersion of flow, that does not survive in the thermodynamic limit. Particularly, the generating function of distance travelled by particles is shown to have universal form, specific for Kardar–Parisi–Zhang universality class. To obtain these quantities we apply the method of calculation of finite size corrections to the infinite system size solution based on the Bethe ansatz solution of master equation.