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Hydrodynamic equation for a deposition model. (English) Zbl 1013.35053
Sidoravicius, Vladas (ed.), In and out of equilibrium. Probability with a physics flavor. Papers from the 4th Brazilian school of probability, Mambucaba, Brazil, August 14-19, 2000. Boston: Birkhäuser. Prog. Probab. 51, 227-248 (2002).
It is shown how a hyperbolic pair of conservation laws, \(\rho_t+(\rho u)_x=0, u_t+\rho_x=0\) is obtained as the formally computed hydrodynamic limit of some randomly growing interface models. The basic structural properties of this system are given.
For the entire collection see [Zbl 0996.00040].

35L65 Hyperbolic conservation laws
82C41 Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics
60K35 Interacting random processes; statistical mechanics type models; percolation theory