On diffusivity of a tagged particle in asymmetric zero-range dynamics
Sethuraman, Sunder
Annales de l'I.H.P. Probabilités et statistiques, Tome 43 (2007), p. 215-232 / Harvested from Numdam
@article{AIHPB_2007__43_2_215_0,
     author = {Sethuraman, Sunder},
     title = {On diffusivity of a tagged particle in asymmetric zero-range dynamics},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {43},
     year = {2007},
     pages = {215-232},
     doi = {10.1016/j.anihpb.2006.03.002},
     mrnumber = {2303120},
     zbl = {1112.60084},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2007__43_2_215_0}
}
Sethuraman, Sunder. On diffusivity of a tagged particle in asymmetric zero-range dynamics. Annales de l'I.H.P. Probabilités et statistiques, Tome 43 (2007) pp. 215-232. doi : 10.1016/j.anihpb.2006.03.002. http://gdmltest.u-ga.fr/item/AIHPB_2007__43_2_215_0/

[1] E.D. Andjel, Invariant measures for the zero range process, Ann. Probab. 10 (1982) 525-547. | MR 659526 | Zbl 0492.60096

[2] R. Arratia, The motion of a tagged particle in the simple symmetric exclusion system on Z 1 , Ann. Probab. 11 (1983) 362-373. | MR 690134 | Zbl 0515.60097

[3] A. De Masi, P. Ferrari, Self-diffusion in one-dimensional lattice gases in the presence of an external field, J. Statist. Phys. 38 (1985) 603-613. | MR 788435 | Zbl 0624.60117

[4] S. Ethier, T. Kurtz, Markov Processes: Characterization and Convergence, J. Wiley and Sons, New York, 1986. | MR 838085 | Zbl 0592.60049

[5] P. Ferrari, Limit theorems for tagged particles, Markov Processes Related Fields 2 (1996) 17-40. | MR 1418405 | Zbl 0879.60109

[6] S. Grosskinsky, G.M. Schütz, H. Spohn, Condensation in the zero range process: stationary and dynamical properties, J. Statist. Phys. 113 (2003) 389-410. | MR 2013129 | Zbl 1081.82010

[7] M. Jara, C. Landim, Nonequilibrium central limit theorem for a tagged particle in symmetric simple exclusion, Ann. Inst. H. Poincaré Probab. Statist., in press. | Numdam | MR 2259975 | Zbl 1101.60080

[8] I. Jeon, P. March, B. Pittel, Size of the largest cluster under zero-range invariant measures, Ann. Probab. 28 (2000) 1162-1194. | MR 1797308 | Zbl 1023.60084

[9] C. Kipnis, Central limit theorems for infinite series of queues and applications to simple exclusion, Ann. Probab. 14 (1986) 397-408. | MR 832016 | Zbl 0601.60098

[10] C. Kipnis, C. Landim, Scaling Limits of Interacting Particle Systems, Grundlehren der Mathematischen Wissenschaften, vol. 320, Springer-Verlag, Berlin, 1999. | MR 1707314 | Zbl 0927.60002

[11] C. Kipnis, S.R.S. Varadhan, Central limit theorem for additive functionals of reversible Markov processes, Comm. Math. Phys. 104 (1986) 1-19. | MR 834478 | Zbl 0588.60058

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

[13] C. Landim, S. Sethuraman, S.R.S. Varadhan, Spectral gap for zero range dynamics, Ann. Probab. 24 (1996) 1871-1902. | MR 1415232 | Zbl 0870.60095

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

[15] C. Landim, S. Volchan, Equilibrium fluctuations for a driven tracer particle dynamics, Stochastic Process Appl. 85 (2000) 139-158. | MR 1730614 | Zbl 0997.60121

[16] T.M. Liggett, An infinite particle system with zero range interactions, Ann. Probab. 1 (1973) 240-253. | MR 381039 | Zbl 0264.60083

[17] T.M. Liggett, Interacting Particle Systems, Grundlehren der Mathematischen Wissenschaften, vol. 276, Springer-Verlag, New York, 1985. | MR 776231 | Zbl 0559.60078

[18] T.M. Liggett, Stochastic Interacting Systems: Contact, Voter and Exclusion Processes, Grundlehren der Mathematischen Wissenschaften, vol. 324, Springer-Verlag, Berlin, 1999. | MR 1717346 | Zbl 0949.60006

[19] B. Morris, Spectral gap for the zero range process with constant rate, preprint, math.PR/0405161. | MR 2271475 | Zbl 1111.60077

[20] C.M. Newman, A General Central Limit Theorem for FKG systems, Comm. Math. Phys. 91 (1983) 75-80. | MR 719811 | Zbl 0528.60024

[21] C.M. Newman, Asymptotic independence and limit theorems for positively and negatively dependent random variables, in: Inequalities in Statistics and Probability, IMS Lecture Notes Monograph Series, vol. 5, 1984, pp. 127-140. | MR 789244

[22] S. Olla, Homogenization of diffusion processes in random fields, École Polytechnique Lecture Notes, 1994.

[23] S.C. Port, C.J. Stone, Infinite particle systems, Trans. Amer. Math. Soc. 178 (1973) 307-340. | MR 326868 | Zbl 0283.60057

[24] J. Quastel, F. Rezakhanlou, S.R.S. Varadhan, Large deviations for the symmetric simple exclusion process in dimensions d3, Probab. Theory Related Fields 113 (1999) 1-84. | MR 1670733 | Zbl 0928.60087

[25] F. Rezakhanlou, Propagation of chaos for symmetric simple exclusions, Comm. Pure Appl. Math. 47 (1994) 943-957. | MR 1283878 | Zbl 0808.60083

[26] F. Rezakhanlou, Evolution of tagged particles in non-reversible particle systems, Comm. Math. Phys. 165 (1994) 1-32. | MR 1298939 | Zbl 0811.60094

[27] H. Rost, M.E. Vares, Hydrodynamics of a one dimensional nearest neighbor model, Contemp. Math. 41 (1985) 329-342. | MR 814722 | Zbl 0572.60095

[28] E. Saada, Processus de zero range et d'exclusion simple avec particule marquee, Ph.D. Thesis, 3rd Cycle, L'Universite Pierre et Marie Curie Paris 6, 1985.

[29] E. Saada, A limit theorem for the position of a tagged particle in a simple exclusion process, Ann. Probab. 15 (1) (1987) 375-381. | MR 877609 | Zbl 0617.60096

[30] E. Saada, Processus de zero-range avec particule marquee, Ann. Inst. H. Poincaré 26 (1990) 5-17. | Numdam | MR 1075436 | Zbl 0703.60101

[31] T. Seppäläinen, Coupling the totally asymmetric simple exclusion process with a moving interface, Markov Process Related Fields 4 (1998) 593-628. | MR 1677061 | Zbl 0922.60094

[32] S. Sethuraman, On extremal measures for conservative particle systems, Ann. Inst. H. Poincaré Probab. Statist. 37 (2001) 139-154. | Numdam | MR 1819121 | Zbl 0981.60098

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

[34] S. Sethuraman, L. Xu, A central limit theorem for reversible exclusion and zero-range particle systems, Ann. Probab. 24 (1996) 1842-1870. | MR 1415231 | Zbl 0872.60079

[35] F. Spitzer, Interaction of Markov processes, Adv. Math. 5 (1970) 246-290. | MR 268959 | Zbl 0312.60060

[36] H. Spohn, Large Scale Dynamics of Interacting Particles, Springer-Verlag, Berlin, 1991. | Zbl 0742.76002

[37] 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