Abstract
We obtain the hydrodynamic limit of a simple exclusion process in an inhomogeneous environment of divergence form. Our main assumption is a suitable version of Γ-convergence for the environment. In this way we obtain an unified approach to recent works on the field.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Faggionato, A.: Bulk diffusion of 1D exclusion process with bond disorder. Markov Process. Relat. Fields 13(3), 519–542 (2007)
Faggionato, A., Jara, M., Landim, C.: Hydrodynamic behavior of 1D subdiffusive exclusion processes with random conductances. Probab. Theory Relat. Fields 144(3–4), 633–667 (2009)
Faggionato, A.: Random walks and exclusion processes among random conductances on random infinite clusters: homogenization and hydrodynamic limit. Electron. J. Probab. 13, 2217–2247 (2008)
Faggionato, A., Martinelli, F.: Hydrodynamic limit of a disordered lattice gas. Probab. Theory Relat. Fields 127(4), 535–608 (2003)
Franco, F., Landim, C.: Hydrodynamic limit of gradient exclusion processes with conductances. Arch. Rat. Mech. Anal. 195, 409–439 (2010)
Fritz, J.: Hydrodynamics in a symmetric random medium. Comm. Math. Phys. 125(1), 13–25 (1989)
Gonçalves, P., Jara, M.: Scaling limits for gradient systems in random environment. J. Stat. Phys. 131(4), 691–716 (2008)
Gonçalves, P., Jara, M.: Scaling limits of a tagged particle in the exclusion process with variable diffusion coefficient. J. Stat. Phys. 132(6), 1135–1143 (2008)
Guo, M.Z., Papanicolaou, G.C., Varadhan, S.R.S.: Nonlinear diffusion limit for a system with nearest neighbor interactions. Comm. Math. Phys. 118(1), 31–59 (1988)
Jara, M.D., Landim, C.: Nonequilibrium central limit theorem for a tagged particle in symmetric simple exclusion. Ann. Inst. H. Poincaré Probab. Statist. 42(5), 567–577 (2006)
Jara, M.: Finite-dimensional approximation for the diffusion coefficient in the simple exclusion process. Ann. Probab. 34(6), 2365–2381 (2006)
Kigami, J.: Analysis on fractals, volume 143 of Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge (2001)
Kipnis, C., Landim, C.: Scaling limits of interacting particle systems, volume 320 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer, Berlin (1999)
Koukkous, A.: Hydrodynamic behavior of symmetric zero-range processes with random rates. Stoch. Process. Appl. 84(2), 297–312 (1999)
Nagy, K.: Symmetric random walk in random environment in one dimension. Period. Math. Hung. 45(1–2), 101–120 (2002)
Papanicolaou, G.C., Varadhan, S.R.S.: Diffusions with random coefficients. In: Statistics and probability: essays in honor of C. R. Rao, pp. 547–552. North-Holland, Amsterdam (1982)
Quastel, J.: Bulk diffusion in a system with site disorder. Ann. Probab. 34(5), 1990–2036 (2006)
Tartar, L.: Homogénéisation et compacité par compensation. In: Séminaire Goulaouic-Schwartz (1978/1979), pages Exp. No. 9, 9. École Polytech., Palaiseau (1979)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jara, M. (2011). Hydrodynamic Limit of the Exclusion Process in Inhomogeneous Media. In: Peixoto, M., Pinto, A., Rand, D. (eds) Dynamics, Games and Science II. Springer Proceedings in Mathematics, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14788-3_33
Download citation
DOI: https://doi.org/10.1007/978-3-642-14788-3_33
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14787-6
Online ISBN: 978-3-642-14788-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)