First order correction for the hydrodynamic limit of symmetric simple exclusion processes with speed change in dimension \(d\geq 3\). (English) Zbl 0935.60096

Summary: The hydrodynamic limit of the symmetric simple exclusion process with speed change is given by a diffusive equation in the appropriate scale. Following the nongradient method introduced by S. R. S. Varadhan [in: Asymptotic problems in probability theory: stochastic models and diffusions on fractals. Pitman Res. Notes Math. Ser. 283, 75-128 (1993; Zbl 0793.60105)] and the Navier-Stokes methods developed by H.-T. Yau [Lett. Math. Phys. 22, No. 1, 63-80 (1991; Zbl 0725.60120)], we prove that in the same scale, the next order correction is given by a third order equation for dimension \(d\geq 3\).


60K35 Interacting random processes; statistical mechanics type models; percolation theory
82C22 Interacting particle systems in time-dependent statistical mechanics
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