Exact connections between current fluctuations and the second class particle in a class of deposition models. (English) Zbl 1147.82348

Summary: We consider a large class of nearest neighbor attractive stochastic interacting systems that includes the asymmetric simple exclusion, zero range, bricklayers’ and the symmetric K-exclusion processes. We provide exact formulas that connect particle flux (or surface growth) fluctuations to the two-point function of the process and to the motion of the second class particle. Such connections have only been available for simple exclusion where they were of great use in particle current fluctuation investigations.


82C22 Interacting particle systems in time-dependent statistical mechanics
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[1] E. D. Andjel, Invariant measures for the zero range process. Ann. Probab. 10(3):325–547 (1982). · Zbl 0492.60096
[2] M. Balázs, Growth fluctuations in a class of deposition models. Ann. Inst. H. Poincaré Probab. Statist. 39:639–685 (2003). · Zbl 1029.60075
[3] M. Balázs, E. Cator and T. Seppäläinen, Cube root fluctuations for the corner growth model associated to the exclusion process. Electron. J. Probab. 11:1094–1132 (2006). · Zbl 1139.60046
[4] M. Balázs, F. Rassoul-Agha, T. Seppäläinen, and S. Sethuraman, Existence of the zero range process and a deposition model with superlinear growth rates. To appear in Ann. Probab., http:// arxiv.org/abs/math.PR/0511287 (2006).
[5] M. Balázs and T. Seppäläinen, Order of current variance and diffusivity in the asymmetric simple exclusion process. Submitted, http://arxiv.org/abs/math.PR/0608400 (2006).
[6] L. Booth, Random Spatial Structures and Sums. PhD thesis, Utrecht University (2002). · Zbl 1040.35122
[7] C. Cocozza-Thivent, Processus des misanthropes. Z. Wahrsch. Verw. Gebiete 70:509–523 (1985). · Zbl 0554.60097
[8] P. A. Ferrari and L. R. G. Fontes, Current fluctuations for the asymmetric simple exclusion process. Ann. Probab. 22:820–832 (1994). · Zbl 0806.60099
[9] P. L. Ferrari and H. Spohn, Scaling limit for the space-time covariance of the stationary totally asymmetric simple exclusion process. Comm. Math. Phys. 265(1):1–44 (2006). · Zbl 1118.82032
[10] T. M. Liggett, An infinite particle system with zero range interactions. Ann. Probab. 1(2):240–253 (1973). · Zbl 0264.60083
[11] T. M. Liggett, Interacting Particle Systems (Springer-Verlag, 1985). · Zbl 0559.60078
[12] M. Prähofer and H. Spohn, Current fluctuations for the totally asymmetric simple exclusion process. In In and out of equilibrium (Mambucaba, 2000), Vol. 51 of Progr. Probab. (Birkhäuser Boston, Boston, MA, 2002, pp. 185–204). · Zbl 1015.60093
[13] C. Quant, On the construction and stationary distributions of some spatial queueing and particle systems. PhD thesis, Utrecht University, 2002.
[14] J. Quastel and B. Valkó, t1/3 Superdiffusivity of finite-range asymmetric exclusion processes on \(\mathbb{Z}\). To appear in Comm. Math. Phys. http://arxiv.org/abs/math.PR/0605266 (2006).
[15] F. Rezakhanlou, Hydrodynamic limit for attractive particle systems on \(\mathbb{Z}\)d. Comm. Math. Phys. 140(3):417–448 (1991). · Zbl 0738.60098
[16] F. Spitzer, Interaction of Markov processes. Adv. Math. 5:246–290 (1970). · Zbl 0312.60060
[17] H. Spohn, Large Scale Dynamics of Interacting Particles. Texts and Monographs in Physics (Springer Verlag, Heidelberg, 1991). · Zbl 0742.76002
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