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

Mikhail Tamm 1, Sergei K. Nechaev 2, 3, Satya N. Majumdar 2

Journal of Physics A Mathematical and Theoretical 44 (2011) 012002

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.

  • 1. Physics Department,
    Moscow State University
  • 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 3. P. N. Lebedev Physical Institute,
    Russian Academy of Science