Strong law of large numbers for the interface in ballistic deposition

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1. [1] Bahadoran C., Hydrodynamical limit for spatially heterogeneous simple exclusion process, Probab. Theory Related Fields110 (1998) 287-331. Zbl0929.60082MR1616563
2. [2] Benjamini I., Ferrari P., Landim C., Asymmetric conservative processes with random rates, Stochastic Process. Appl.61 (1996) 181-204. Zbl0849.60093MR1386172
3. [3] Crandall M.G., Evans L.C., Lions P.L., Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc.282 (1984) 487-502. Zbl0543.35011MR732102
4. [4] Crandall M.G., Lions P.L., Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc.277 (1983) 1-42. Zbl0599.35024MR690039
5. [5] De Masi A., Presutti E., Mathematical Methods for Hydrodynamic Limits, Lecture Notes in Mathematics, Vol. 1501, Springer, Berlin, 1991. Zbl0754.60122MR1175626
6. [6] Durrett R., Ten lectures on particle systems, in: Lecture Notes in Mathematics, Vol. 1608, Springer, 1995, pp. 97-201 (Saint-Flour, 1993). Zbl0840.60088MR1383122
7. [7] Durrett R., Liggett T., The shape of the limit set in Richardson's growth model, Ann. Probab.9 (1981) 186-193. Zbl0457.60083MR606981
8. [8] Evans L.C., Partial Differential Equations, American Mathematical Society, 1998. Zbl0902.35002MR1625845
9. [9] Griffeath D., Additive and Cancellative Interacting Particle Systems, Lecture Notes in Mathematics, Vol. 724, Springer, 1979. Zbl0412.60095MR538077
10. [10] Grimmett G., Kesten H., First-passage percolation, network flows and electrical resistances, Z. Wahrsch. Verw. Gebiete66 (1984) 335-366. Zbl0525.60098MR751574
11. [11] Harris T.E., Nearest-neighbor Markov interaction processes on multidimensional lattices, Adv. Math.9 (1972) 66-89. Zbl0267.60107MR307392
12. [12] Ishii H., Uniqueness of unbounded viscosity solutions of Hamilton-Jacobi equations, Indiana Univ. Math. J.33 (1984) 721-748. Zbl0551.49016MR756156
13. [13] Kesten H., Aspects of first-passage percolation, in: Lecture Notes in Mathematics, Vol. 1180, Springer, 1986, pp. 125-264. Zbl0602.60098MR876084
14. [14] Kesten H., On the speed of convergence in first-passage percolation, Ann. Appl. Probab.3 (1993) 296-338. Zbl0783.60103MR1221154
15. [15] Kipnis C., Landim C., Scaling Limits of Interacting Particle Systems, Grundlehren der mathematischen Wissenschaften, Vol. 320, Springer, Berlin, 1999. Zbl0927.60002MR1707314
16. [16] Krug J., Meakin P., Microstructure and surface scaling in ballistic deposition at oblique incidence, Physical Review A40 (1989) 2064-2077. 
17. [17] Krug J., Meakin P., Columnar growth in oblique incidence ballistic deposition: Faceting, noise reduction, and mean-field theory, Physical Review A43 (1991) 900-919. 
18. [18] Krug J., Spohn H., Kinetic roughening of growing surfaces, in: Godrèche C. (Ed.), Solids far from Equilibrium, Cambridge University Press, 1991, pp. 479-582. 
19. [19] Liggett T.M., Interacting Particle Systems, Springer, New York, 1985. Zbl0559.60078MR776231
20. [20] Meakin P., Ramanlal P., Sander L.M., Ball R.C., Ballistic deposition on surfaces, Physical Review A34 (1986) 5091-5103. 
21. [21] Rezakhanlou F., Continuum limit for some growth models, Preprint, 1999. Zbl1081.82016MR1921440
22. [22] Rockafellar R.T., Convex Analysis, Princeton University Press, 1970. Zbl0193.18401MR274683
23. [23] Rost H., Non-equilibrium behaviour of a many particle process: Density profile and local equilibrium, Z. Wahrsch. Verw. Gebiete58 (1981) 41-53. Zbl0451.60097MR635270
24. [24] Seppäläinen T., Exact limiting shape for a simplified model of first-passage percolation on the plane, Ann. Probab.26 (1998) 1232-1250. Zbl0935.60093MR1640344
25. [25] Seppäläinen T., Coupling the totally asymmetric simple exclusion process with a moving interface (I Escola Brasileira de Probabilidade, IMPA, Rio de Janeiro, 1997), Markov Process. Related Fields4 (1998) 593-628. Zbl0922.60094MR1677061
26. [26] Seppäläinen T., Existence of hydrodynamics for the totally asymmetric simple K-exclusion process, Ann. Probab.27 (1999) 361-415. Zbl0947.60088MR1681094
27. [27] Seppäläinen T., Krug J., Hydrodynamics and platoon formation for a totally asymmetric exclusion model with particlewise disorder, J. Statist. Phys.95 (1999) 529-571. Zbl0964.82041MR1700871
28. [28] Smythe R.T., Wierman J.C., First-passage percolation on the square lattice, Lecture Notes in Mathematics, Vol. 671, Springer, 1978. Zbl0379.60001MR513421
29. [29] Spohn H., Large Scale Dynamics of Interacting Particles, Springer, Berlin, 1991. Zbl0742.76002
30. [30] Talagrand M., Concentration of measure and isoperimetric inequalities in product spaces, Inst. Hautes Études Sci. Publ. Math.81 (1995) 73-205. Zbl0864.60013MR1361756