Hydrodynamic limits of interacting particle systems on crystal lattices in periodic realizations. (English) Zbl 1524.60267

Guan, Zehao

Electron. J. Probab. 28, Paper No. 97, 30 p. (2023).

Summary: We study the hydrodynamic limits of the simple exclusion processes and the zero range processes on crystal lattices. For a periodic realization of crystal lattice, we derive the hydrodynamic limit for the exclusion processes and the zero range processes, which depends on both the structure of crystal lattice and its embedding into \(\mathbb{R}^d\). Even through the crystal lattices have inhomogeneous local structure, for all periodic realizations, we apply the entropy method to derive the hydrodynamic limits. Also, we discuss how the limit equation depends on the choices of the realizations.

MSC:

60K35	Interacting random processes; statistical mechanics type models; percolation theory
58E20	Harmonic maps, etc.
82C41	Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics
82C22	Interacting particle systems in time-dependent statistical mechanics

Keywords:

crystal lattices; exclusion processes

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