@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}, volume = {36}, year = {2000}, pages = {691-736}, mrnumber = {1797390}, zbl = {0972.60097}, language = {en}, url = {http://dml.mathdoc.fr/item/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) pp. 691-736. http://gdmltest.u-ga.fr/item/AIHPB_2000__36_6_691_0/
[1] Hydrodynamical limit for spatially heterogeneous simple exclusion process, Probab. Theory Related Fields 110 (1998) 287-331. | MR 1616563 | Zbl 0929.60082
,[2] Asymmetric conservative processes with random rates, Stochastic Process. Appl. 61 (1996) 181-204. | MR 1386172 | Zbl 0849.60093
, , ,[3] Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 282 (1984) 487-502. | MR 732102 | Zbl 0543.35011
, , ,[4] Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1983) 1-42. | MR 690039 | Zbl 0599.35024
, ,[5] Mathematical Methods for Hydrodynamic Limits, Lecture Notes in Mathematics, Vol. 1501, Springer, Berlin, 1991. | MR 1175626 | Zbl 0754.60122
, ,[6] Ten lectures on particle systems, in: Lecture Notes in Mathematics, Vol. 1608, Springer, 1995, pp. 97-201 (Saint-Flour, 1993). | MR 1383122 | Zbl 0840.60088
,[7] The shape of the limit set in Richardson's growth model, Ann. Probab. 9 (1981) 186-193. | MR 606981 | Zbl 0457.60083
, ,[8] Partial Differential Equations, American Mathematical Society, 1998. | MR 1625845 | Zbl 0902.35002
,[9] Additive and Cancellative Interacting Particle Systems, Lecture Notes in Mathematics, Vol. 724, Springer, 1979. | MR 538077 | Zbl 0412.60095
,[10] First-passage percolation, network flows and electrical resistances, Z. Wahrsch. Verw. Gebiete 66 (1984) 335-366. | MR 751574 | Zbl 0525.60098
, ,[11] Nearest-neighbor Markov interaction processes on multidimensional lattices, Adv. Math. 9 (1972) 66-89. | MR 307392 | Zbl 0267.60107
,[12] Uniqueness of unbounded viscosity solutions of Hamilton-Jacobi equations, Indiana Univ. Math. J. 33 (1984) 721-748. | MR 756156 | Zbl 0551.49016
,[13] Aspects of first-passage percolation, in: Lecture Notes in Mathematics, Vol. 1180, Springer, 1986, pp. 125-264. | MR 876084 | Zbl 0602.60098
,[14] On the speed of convergence in first-passage percolation, Ann. Appl. Probab. 3 (1993) 296-338. | MR 1221154 | Zbl 0783.60103
,[15] Scaling Limits of Interacting Particle Systems, Grundlehren der mathematischen Wissenschaften, Vol. 320, Springer, Berlin, 1999. | MR 1707314 | Zbl 0927.60002
, ,[16] Microstructure and surface scaling in ballistic deposition at oblique incidence, Physical Review A 40 (1989) 2064-2077.
, ,[17] Columnar growth in oblique incidence ballistic deposition: Faceting, noise reduction, and mean-field theory, Physical Review A 43 (1991) 900-919.
, ,[18] Kinetic roughening of growing surfaces, in: Godrèche C. (Ed.), Solids far from Equilibrium, Cambridge University Press, 1991, pp. 479-582.
, ,[19] Interacting Particle Systems, Springer, New York, 1985. | MR 776231 | Zbl 0559.60078
,[20] Ballistic deposition on surfaces, Physical Review A 34 (1986) 5091-5103.
, , , ,[21] Continuum limit for some growth models, Preprint, 1999. | MR 1921440
,[22] Convex Analysis, Princeton University Press, 1970. | MR 274683 | Zbl 0193.18401
,[23] Non-equilibrium behaviour of a many particle process: Density profile and local equilibrium, Z. Wahrsch. Verw. Gebiete 58 (1981) 41-53. | MR 635270 | Zbl 0451.60097
,[24] Exact limiting shape for a simplified model of first-passage percolation on the plane, Ann. Probab. 26 (1998) 1232-1250. | MR 1640344 | Zbl 0935.60093
,[25] 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 1677061 | Zbl 0922.60094
,[26] Existence of hydrodynamics for the totally asymmetric simple K-exclusion process, Ann. Probab. 27 (1999) 361-415. | MR 1681094 | Zbl 0947.60088
,[27] Hydrodynamics and platoon formation for a totally asymmetric exclusion model with particlewise disorder, J. Statist. Phys. 95 (1999) 529-571. | MR 1700871 | Zbl 0964.82041
, ,[28] First-passage percolation on the square lattice, Lecture Notes in Mathematics, Vol. 671, Springer, 1978. | MR 513421 | Zbl 0379.60001
, ,[29] Large Scale Dynamics of Interacting Particles, Springer, Berlin, 1991. | Zbl 0742.76002
,[30] Concentration of measure and isoperimetric inequalities in product spaces, Inst. Hautes Études Sci. Publ. Math. 81 (1995) 73-205. | Numdam | MR 1361756 | Zbl 0864.60013
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