On diffusivity of a tagged particle in asymmetric zero-range dynamics

Sunder Sethuraman

Annales de l'I.H.P. Probabilités et statistiques (2007)

  • Volume: 43, Issue: 2, page 215-232
  • ISSN: 0246-0203

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Sethuraman, Sunder. "On diffusivity of a tagged particle in asymmetric zero-range dynamics." Annales de l'I.H.P. Probabilités et statistiques 43.2 (2007): 215-232. <http://eudml.org/doc/77932>.

@article{Sethuraman2007,
author = {Sethuraman, Sunder},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {zero-range; diffusive; variance; invariance principle},
language = {eng},
number = {2},
pages = {215-232},
publisher = {Elsevier},
title = {On diffusivity of a tagged particle in asymmetric zero-range dynamics},
url = {http://eudml.org/doc/77932},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Sethuraman, Sunder
TI - On diffusivity of a tagged particle in asymmetric zero-range dynamics
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2007
PB - Elsevier
VL - 43
IS - 2
SP - 215
EP - 232
LA - eng
KW - zero-range; diffusive; variance; invariance principle
UR - http://eudml.org/doc/77932
ER -

References

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  1. [1] E.D. Andjel, Invariant measures for the zero range process, Ann. Probab.10 (1982) 525-547. Zbl0492.60096MR659526
  2. [2] R. Arratia, The motion of a tagged particle in the simple symmetric exclusion system on Z 1 , Ann. Probab.11 (1983) 362-373. Zbl0515.60097MR690134
  3. [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. Zbl0624.60117MR788435
  4. [4] S. Ethier, T. Kurtz, Markov Processes: Characterization and Convergence, J. Wiley and Sons, New York, 1986. Zbl0592.60049MR838085
  5. [5] P. Ferrari, Limit theorems for tagged particles, Markov Processes Related Fields2 (1996) 17-40. Zbl0879.60109MR1418405
  6. [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. Zbl1081.82010MR2013129
  7. [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. Zbl1101.60080MR2259975
  8. [8] I. Jeon, P. March, B. Pittel, Size of the largest cluster under zero-range invariant measures, Ann. Probab.28 (2000) 1162-1194. Zbl1023.60084MR1797308
  9. [9] C. Kipnis, Central limit theorems for infinite series of queues and applications to simple exclusion, Ann. Probab.14 (1986) 397-408. Zbl0601.60098MR832016
  10. [10] C. Kipnis, C. Landim, Scaling Limits of Interacting Particle Systems, Grundlehren der Mathematischen Wissenschaften, vol. 320, Springer-Verlag, Berlin, 1999. Zbl0927.60002MR1707314
  11. [11] C. Kipnis, S.R.S. Varadhan, Central limit theorem for additive functionals of reversible Markov processes, Comm. Math. Phys.104 (1986) 1-19. Zbl0588.60058MR834478
  12. [12] C. Landim, S. Olla, S. Volchan, Driven tracer particle in one dimensional symmetric simple exclusion process, Comm. Math. Phys.192 (1998) 287-307. Zbl0911.60085MR1617558
  13. [13] C. Landim, S. Sethuraman, S.R.S. Varadhan, Spectral gap for zero range dynamics, Ann. Probab.24 (1996) 1871-1902. Zbl0870.60095MR1415232
  14. [14] C. Landim, H.T. Yau, Fluctuation–dissipation equation of asymmetric simple exclusion processes, Probab. Theory Related Fields108 (1997) 321-356. Zbl0884.60092
  15. [15] C. Landim, S. Volchan, Equilibrium fluctuations for a driven tracer particle dynamics, Stochastic Process Appl.85 (2000) 139-158. Zbl0997.60121MR1730614
  16. [16] T.M. Liggett, An infinite particle system with zero range interactions, Ann. Probab.1 (1973) 240-253. Zbl0264.60083MR381039
  17. [17] T.M. Liggett, Interacting Particle Systems, Grundlehren der Mathematischen Wissenschaften, vol. 276, Springer-Verlag, New York, 1985. Zbl0559.60078MR776231
  18. [18] T.M. Liggett, Stochastic Interacting Systems: Contact, Voter and Exclusion Processes, Grundlehren der Mathematischen Wissenschaften, vol. 324, Springer-Verlag, Berlin, 1999. Zbl0949.60006MR1717346
  19. [19] B. Morris, Spectral gap for the zero range process with constant rate, preprint, math.PR/0405161. Zbl1111.60077MR2271475
  20. [20] C.M. Newman, A General Central Limit Theorem for FKG systems, Comm. Math. Phys.91 (1983) 75-80. Zbl0528.60024MR719811
  21. [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. MR789244
  22. [22] S. Olla, Homogenization of diffusion processes in random fields, École Polytechnique Lecture Notes, 1994. 
  23. [23] S.C. Port, C.J. Stone, Infinite particle systems, Trans. Amer. Math. Soc.178 (1973) 307-340. Zbl0283.60057MR326868
  24. [24] J. Quastel, F. Rezakhanlou, S.R.S. Varadhan, Large deviations for the symmetric simple exclusion process in dimensions d 3 , Probab. Theory Related Fields113 (1999) 1-84. Zbl0928.60087MR1670733
  25. [25] F. Rezakhanlou, Propagation of chaos for symmetric simple exclusions, Comm. Pure Appl. Math.47 (1994) 943-957. Zbl0808.60083MR1283878
  26. [26] F. Rezakhanlou, Evolution of tagged particles in non-reversible particle systems, Comm. Math. Phys.165 (1994) 1-32. Zbl0811.60094MR1298939
  27. [27] H. Rost, M.E. Vares, Hydrodynamics of a one dimensional nearest neighbor model, Contemp. Math.41 (1985) 329-342. Zbl0572.60095MR814722
  28. [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. [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. Zbl0617.60096MR877609
  30. [30] E. Saada, Processus de zero-range avec particule marquee, Ann. Inst. H. Poincaré26 (1990) 5-17. Zbl0703.60101MR1075436
  31. [31] T. Seppäläinen, Coupling the totally asymmetric simple exclusion process with a moving interface, Markov Process Related Fields4 (1998) 593-628. Zbl0922.60094MR1677061
  32. [32] S. Sethuraman, On extremal measures for conservative particle systems, Ann. Inst. H. Poincaré Probab. Statist.37 (2001) 139-154. Zbl0981.60098MR1819121
  33. [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. Zbl1029.60084MR1755948
  34. [34] S. Sethuraman, L. Xu, A central limit theorem for reversible exclusion and zero-range particle systems, Ann. Probab.24 (1996) 1842-1870. Zbl0872.60079MR1415231
  35. [35] F. Spitzer, Interaction of Markov processes, Adv. Math.5 (1970) 246-290. Zbl0312.60060MR268959
  36. [36] H. Spohn, Large Scale Dynamics of Interacting Particles, Springer-Verlag, Berlin, 1991. Zbl0742.76002
  37. [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. Zbl0816.60093MR1340041

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