Statistics of layered zigzags: a two-dimensional generalization of TASEP

A novel discrete growth model in 2+1 dimensions is presented in three equivalent formulations: (i) directed motion of zigzags on a cylinder, (ii) interacting interlaced TASEP layers and (iii) growing heap over 2D substrate with a restricted minimal local height gradient. We demonstrate that the coarse-grained behavior of this model is described by the two-dimensional Kardar-Parisi-Zhang equation. The coefficients of different terms in this hydrodynamic equation can be derived from the steady state flow-density curve, the so-called fundamental diagram. A conjecture concerning the analytical form of this flow-density curve is presented and is verified numerically. (fast track communication)