Mobility and Einstein relation for a tagged particle in asymmetric mean zero random walk with simple exclusion
Annales de l'I.H.P. Probabilités et statistiques, Volume 41 (2005) no. 2, p. 237-254
@article{AIHPB_2005__41_2_237_0,
     author = {Loulakis, Michail},
     title = {Mobility and Einstein relation for a tagged particle in asymmetric mean zero random walk with simple exclusion},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Elsevier},
     volume = {41},
     number = {2},
     year = {2005},
     pages = {237-254},
     doi = {10.1016/j.anihpb.2004.07.001},
     zbl = {1108.60082},
     mrnumber = {2124642},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2005__41_2_237_0}
}
Loulakis, Michail. Mobility and Einstein relation for a tagged particle in asymmetric mean zero random walk with simple exclusion. Annales de l'I.H.P. Probabilités et statistiques, Volume 41 (2005) no. 2, pp. 237-254. doi : 10.1016/j.anihpb.2004.07.001. http://www.numdam.org/item/AIHPB_2005__41_2_237_0/

[1] P.A. Ferrari, S. Goldstein, J.L. Lebowitz, Diffusion, mobility and the Einstein relation, in: Fritz J., Jaffe A., Száz D. (Eds.), Statistical Physics and Dynamical Systems, Birkhäuser, Boston, 1985, pp. 405-441. | MR 821308 | Zbl 0559.60065

[2] M.Z. Guo, G.C. Papanicolaou, S.R.S. Varadhan, Nonlinear diffusion limit for a system with nearest neighbor interactions, Comm. Math. Phys. 118 (1988) 31-59. | MR 954674 | Zbl 0652.60107

[3] C. Kipnis, C. Landim, Scaling Limits of Interacting Particle Systems, Grundlehren Math. Wiss., Springer-Verlag, 1999. | MR 1707314 | Zbl 0927.60002

[4] C. Kipnis, S.R.S. Varadhan, Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusion, Comm. Math. Phys. 106 (1986) 1-19. | MR 834478 | Zbl 0588.60058

[5] T. Komorowski, S. Olla, On mobility and Einstein relation for tracers in time-mixing random environments, J. Statist. Phys., in press, preprint available at http://www.ceremade.dauphine.fr/~olla. | MR 2123642 | Zbl 02171847

[6] C. Landim, S. Olla, S.R.S. Varadhan, Finite dimensional approximation of the self-diffusion coefficient for the exclusion process, Ann. Probab. 30 (2) (2002) 483-508. | MR 1905849 | Zbl 1018.60097

[7] C. Landim, S. Olla, S.R.S. Varadhan, Symmetric simple exclusion process: regularity of the self diffusion coefficient, Comm. Math. Phys. 224 (1) (2001) 307-321. | MR 1869001 | Zbl 0994.60093

[8] C. Landim, S. Olla, S.R.S. Varadhan, Asymptotic behavior of a tagged particle in simple exclusion processes, Bol. Soc. Brasil. Mat. (N.S.) 31 (3) (2000) 241-275. | MR 1817088 | Zbl 0983.60100

[9] C. Landim, S. Olla, S.B. Volchan, Driven tracer particle in 1 dimensional symmetric simple exclusion, Comm. Math. Phys. 192 (2) (1998) 287-307. | MR 1617558 | Zbl 0911.60085

[10] C. Landim, H.T. Yau, Fluctuation-dissipation equation of asymmetric simple exclusion processes, Probab. Theory Related Fields 108 (1997) 321-356. | MR 1465163 | Zbl 0884.60092

[11] J.L. Lebowitz, H. Rost, The Einstein relation for the displacement of a test particle in a random environment, Stochastic Process. Appl. 54 (1994) 183-196. | MR 1307334 | Zbl 0812.60096

[12] T. Liggett, Interacting Particle Systems, Grundlehren Math. Wiss., Springer-Verlag, New York, 1985. | MR 776231 | Zbl 0559.60078

[13] M. Loulakis, Einstein relation for a tagged particle in simple exclusion processes, Comm. Math. Phys. 229 (2) (2002) 347-367. | MR 1923179 | Zbl 1005.60098

[14] J. Quastel, Diffusion of color in the simple exclusion process, Comm. Pure Appl. Math. 45 (6) (1992) 623-679. | MR 1162368 | Zbl 0769.60097

[15] E. Saada, A limit theorem for the position of a tagged particle in a simple exclusion process, Ann. Probab. 15 (1987) 375-381. | MR 877609 | Zbl 0617.60096

[16] S. Sethuraman, H.T. Yau, S.R.S. Varadhan, Diffusive limit of a tagged particle in asymmetric simple exclusion processes, Comm. Pure Appl. Math. 53 (2000) 972-1006. | MR 1755948 | Zbl 1029.60084

[17] R.M. Sued, Regularity properties of the diffusion coefficient for a mean zero exclusion process, IMPA Thesis, available at: http://www.preprint.impa.br.

[18] S.R.S. Varadhan, Self diffusion of a tagged particle in equilibrium for asymmetric mean zero random walk with simple exclusion, Ann. Inst. H. Poincaré Probab. Statist. 31 (1995) 273-285. | Numdam | MR 1340041 | Zbl 0816.60093