Abstract
We consider the asymmetric simple exclusion process. We review some results in dimension d≥3 concerning the fluctuation-dissipation theorem and we prove regularity of viscosity coefficients.
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REFERENCES
C. Bernardin, Regularity of the diffusion coefficient for lattice gas reversible under Bernoulli measures, Stochastic Process. Appl. 101:43–68 (2002).
C. C. Chang, C. Landim, and S. Olla, Equilibrium fluctuations of asymmetric exclusion processes in dimension d≧3, Probab. Theory Related Fields 119:381–409 (2001).
R. Esposito, R. Marra, and H. T. Yau, Diffusive limit of asymmetric simple exclusion, Rev. Math. Phys. 6:1233–1267 (1994).
C. Kipnis and C. Landim, Scaling Limit of Interacting Particle Systems (Springer Verlag, Berlin, 1999).
C. Kipnis and S. R. S. Varadhan, Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusion, Comm. Math. Phys. 106:1–19 (1986).
C. Landim, S. Olla, and H. T. Yau, First order correction for the hydrodynamic limit of asymmetric simple exclusion processes in dimension d≧3, Communications on Pure and Applied Mathematics 50:149–203 (1997).
C. Landim, S. Olla, and H. T. Yau, Some properties of the diffusion coefficient for asymmetric simple exclusion processes, Ann. Probab. 24:1779–1807 (1996).
C. Landim and H. T. Yau, Fluctuation-dissipation equation of asymmetric simple exclusion processes, Probab. Theory Related Fields 108:321–356 (1997).
C. Landim, S. Olla, and S. R. S. Varadhan, Finite-dimensional approximation of the self-diffusion coefficient for the exclusion process, Ann. Probab. 30:1–26 (2002).
C. Landim, S. Olla, and S. R. S. Varadhan, Asymptotic behavior of a tagged particle in simple exclusion processes, Bol. Soc. Bras. Mat. 31:241–275 (2000).
C. Landim, S. Olla, and S. R. S. Varadhan, Symmetric simple exclusion process: regularity of the self-diffusion coefficient, Comm. Math. Phys. 224:302–321 (2001).
T. M. Liggett, Interacting Particle Systems (Springer Verlag, New York, 1985).
S. Sethuraman, S. R. S. Varadhan, and H. T. Yau, Diffusive limit of a tagged particle in asymmetric exclusion process, Comm. Pure Appl. Math. 53:972–1006 (2000).
H. Spohn, Large Scale Dynamics of Interacting Particles (Springer, 1991).
S. R. S. Varadhan, Non-linear diffusion limit for a system with nearest neighbor interactions. II, in Asymptotic Problems in Probability Theory: Stochastic Models and Diffusion on Fractals, Pitman Research Notes in Mathematics, Vol. 283, K. D. Elworthy and N. Ikeda, eds. (Wiley, New York, 1994), pp. 75–128.
S. R. S. Varadhan, Self diffusion of a tagged particle in equilibrium for asymmetric mean zero random walks with simple exclusion, Ann. Inst. H. Poincaré (Probabilités) 31:273–285 (1995).
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Landim, C., Olla, S. & Varadhan, S.R.S. On Viscosity and Fluctuation-Dissipation in Exclusion Processes. Journal of Statistical Physics 115, 323–363 (2004). https://doi.org/10.1023/B:JOSS.0000019814.73545.28
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DOI: https://doi.org/10.1023/B:JOSS.0000019814.73545.28