First-order correction for the hydrodynamic limit of asymmetric simple exclusion processes in dimension d ≥ 3
✍ Scribed by C. Landim; S. Olla; H. T. Yau
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 356 KB
- Volume
- 50
- Category
- Article
- ISSN
- 0010-3640
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✦ Synopsis
It is well-known that the hydrodynamic limit of the asymmetric simple exclusion is governed by a viscousless Burgers equation in the Euler scale [15]. We prove that, in the same scale, the next-order correction is given by a viscous Burgers equation up to a fixed time T for dimension d ≥ 3 provided that the corresponding viscousless Burger equation has a smooth solution up to time T . The diffusion coefficient was characterized via a variation of the Green-Kubo formula by [17,18,6]. Within the framework of asymmetric simple exclusion, this provides a rigorous verification in a simplified setting that the correction to the Euler equation is given by the Navier-Stokes equation if the time scale is within the Euler scale.