no. 6
Strong law of large numbers for the interface in ballistic deposition
Annales de l'I.H.P. Probabilités et statistiques, Tome 36 (2000) no. 6, pp. 691-736. 
@article{AIHPB_2000__36_6_691_0,
     author = {Sepp\"al\"ainen, Timo},
     title = {Strong law of large numbers for the interface in ballistic deposition},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {691--736},
     publisher = {Gauthier-Villars},
     volume = {36},
     number = {6},
     year = {2000},
     mrnumber = {1797390},
     zbl = {0972.60097},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2000__36_6_691_0/}
}
TY  - JOUR
AU  - Seppäläinen, Timo
TI  - Strong law of large numbers for the interface in ballistic deposition
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2000
SP  - 691
EP  - 736
VL  - 36
IS  - 6
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPB_2000__36_6_691_0/
LA  - en
ID  - AIHPB_2000__36_6_691_0
ER  - 
%0 Journal Article
%A Seppäläinen, Timo
%T Strong law of large numbers for the interface in ballistic deposition
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2000
%P 691-736
%V 36
%N 6
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPB_2000__36_6_691_0/
%G en
%F AIHPB_2000__36_6_691_0
Seppäläinen, Timo. Strong law of large numbers for the interface in ballistic deposition. Annales de l'I.H.P. Probabilités et statistiques, Tome 36 (2000) no. 6, pp. 691-736. http://www.numdam.org/item/AIHPB_2000__36_6_691_0/

[1] Bahadoran C., Hydrodynamical limit for spatially heterogeneous simple exclusion process, Probab. Theory Related Fields 110 (1998) 287-331. | MR | Zbl

[2] Benjamini I., Ferrari P., Landim C., Asymmetric conservative processes with random rates, Stochastic Process. Appl. 61 (1996) 181-204. | MR | Zbl

[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. | MR | Zbl

[4] Crandall M.G., Lions P.L., Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1983) 1-42. | MR | Zbl

[5] De Masi A., Presutti E., Mathematical Methods for Hydrodynamic Limits, Lecture Notes in Mathematics, Vol. 1501, Springer, Berlin, 1991. | MR | Zbl

[6] Durrett R., Ten lectures on particle systems, in: Lecture Notes in Mathematics, Vol. 1608, Springer, 1995, pp. 97-201 (Saint-Flour, 1993). | MR | Zbl

[7] Durrett R., Liggett T., The shape of the limit set in Richardson's growth model, Ann. Probab. 9 (1981) 186-193. | MR | Zbl

[8] Evans L.C., Partial Differential Equations, American Mathematical Society, 1998. | MR | Zbl

[9] Griffeath D., Additive and Cancellative Interacting Particle Systems, Lecture Notes in Mathematics, Vol. 724, Springer, 1979. | MR | Zbl

[10] Grimmett G., Kesten H., First-passage percolation, network flows and electrical resistances, Z. Wahrsch. Verw. Gebiete 66 (1984) 335-366. | MR | Zbl

[11] Harris T.E., Nearest-neighbor Markov interaction processes on multidimensional lattices, Adv. Math. 9 (1972) 66-89. | MR | Zbl

[12] Ishii H., Uniqueness of unbounded viscosity solutions of Hamilton-Jacobi equations, Indiana Univ. Math. J. 33 (1984) 721-748. | MR | Zbl

[13] Kesten H., Aspects of first-passage percolation, in: Lecture Notes in Mathematics, Vol. 1180, Springer, 1986, pp. 125-264. | MR | Zbl

[14] Kesten H., On the speed of convergence in first-passage percolation, Ann. Appl. Probab. 3 (1993) 296-338. | MR | Zbl

[15] Kipnis C., Landim C., Scaling Limits of Interacting Particle Systems, Grundlehren der mathematischen Wissenschaften, Vol. 320, Springer, Berlin, 1999. | MR | Zbl

[16] Krug J., Meakin P., Microstructure and surface scaling in ballistic deposition at oblique incidence, Physical Review A 40 (1989) 2064-2077.

[17] Krug J., Meakin P., Columnar growth in oblique incidence ballistic deposition: Faceting, noise reduction, and mean-field theory, Physical Review A 43 (1991) 900-919.

[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] Liggett T.M., Interacting Particle Systems, Springer, New York, 1985. | MR | Zbl

[20] Meakin P., Ramanlal P., Sander L.M., Ball R.C., Ballistic deposition on surfaces, Physical Review A 34 (1986) 5091-5103.

[21] Rezakhanlou F., Continuum limit for some growth models, Preprint, 1999. | MR

[22] Rockafellar R.T., Convex Analysis, Princeton University Press, 1970. | MR | Zbl

[23] Rost H., Non-equilibrium behaviour of a many particle process: Density profile and local equilibrium, Z. Wahrsch. Verw. Gebiete 58 (1981) 41-53. | MR | Zbl

[24] Seppäläinen T., Exact limiting shape for a simplified model of first-passage percolation on the plane, Ann. Probab. 26 (1998) 1232-1250. | MR | Zbl

[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 Fields 4 (1998) 593-628. | MR | Zbl

[26] Seppäläinen T., Existence of hydrodynamics for the totally asymmetric simple K-exclusion process, Ann. Probab. 27 (1999) 361-415. | MR | Zbl

[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. | MR | Zbl

[28] Smythe R.T., Wierman J.C., First-passage percolation on the square lattice, Lecture Notes in Mathematics, Vol. 671, Springer, 1978. | MR | Zbl

[29] Spohn H., Large Scale Dynamics of Interacting Particles, Springer, Berlin, 1991. | Zbl

[30] Talagrand M., Concentration of measure and isoperimetric inequalities in product spaces, Inst. Hautes Études Sci. Publ. Math. 81 (1995) 73-205. | Numdam | MR | Zbl