A central limit theorem for random walks in random labyrinths
Bezuidenhout, Carol ; Grimmett, Geoffrey
Annales de l'I.H.P. Probabilités et statistiques, Tome 35 (1999), p. 631-683 / Harvested from Numdam
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Publié le : 1999-01-01
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     author = {Bezuidenhout, Carol and Grimmett, Geoffrey},
     title = {A central limit theorem for random walks in random labyrinths},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {35},
     year = {1999},
     pages = {631-683},
     mrnumber = {1705683},
     zbl = {0938.60033},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_1999__35_5_631_0}
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Bezuidenhout, Carol; Grimmett, Geoffrey. A central limit theorem for random walks in random labyrinths. Annales de l'I.H.P. Probabilités et statistiques, Tome 35 (1999) pp. 631-683. http://gdmltest.u-ga.fr/item/AIHPB_1999__35_5_631_0/

[1] P. Antal and A. Pisztora, On the chemical distance for supercritical Bernoulli percolation, Ann. Probab. 24 (1996) 1036-1048. | MR 1404543 | Zbl 0871.60089

[2] H. Van Beijeren, Transport properties of stochastic Lorentz models, Rev. Modern Phys. 54 (1982) 195-234. | MR 641369

[3] H. Van Beijeren and H. Spohn, Transport properties of the one dimensional stochastic Lorentz model. I. Velocity autocorrelation, J. Statist. Phys. 31 (1982) 231-254. | MR 711477

[4] P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968. | MR 233396 | Zbl 0172.21201

[5] L.A. Bunimovich and S.E. Troubetzkoy, Recurrence properties of Lorentz lattice gas cellular automata, J. Statist. Phys. 67 (1992) 289-302. | MR 1159466 | Zbl 0900.60103

[6] R.M. Burton and M. Keane, Density and uniqueness in percolation, Comm. Math. Phys. 121 ( 1989) 501-505. | MR 990777 | Zbl 0662.60113

[7] E.G.D. Cohen, New types of diffusions in lattice gas cellular automata, in: M. Mareschal and B.L. Holian (Eds.), Microscopic Simulations of Complex Hydrodynamical Phenomena, Plenum Press, New York, 1991, pp. 137-152.

[8] E.G.D. Cohen and F. Wang, New results for diffusion in Lorentz lattice gas cellular automata, J. Statist. Phys. 81 (1995) 445-466.

[9] E.G.D. Cohen and F. Wang, Novel phenomena in Lorentz lattice gases, Physica A 219 (1995) 56-87.

[10] A. Demasi, P.A. Ferrari, S. Goldstein and W.D. Wick, Invariance principle for reversible Markov processes with application to diffusion in the percolation regime, in: R.T. Durrett (Ed.), Particle Systems, Random Media and Large Deviations, Contemporary Mathematics No. 41, Amer. Math. Soc., Providence, RI, 1985, pp. 71-85. | MR 814703 | Zbl 0571.60044

[11] A. Demasi, P.A. Ferrari, S. Goldstein and W.D. Wick, An invariance principle for reversible Markov processes. Applications to random motions in random environments, J. Statist. Phys. 55 (1989) 787-855. | MR 1003538 | Zbl 0713.60041

[12] J.L. Doob, Stochastic Processes, Wiley, New York, 1953. | MR 58896 | Zbl 0053.26802

[13] P.G. Doyle and E.L. Snell, Random Walks and Electric Networks, Carus Mathematical Monograph No. 22, AMA, Washington, DC, 1984. | Zbl 0583.60065

[14] P. Ehrenfest, Collected Scientific Papers, M.J. Klein (Ed.), North-Holland, Amsterdam, 1959. | Zbl 0089.18402

[15] S.N. Ethier and T.G. Kurtz, Markov Processes, Characterization and Convergence, Wiley, New York, 1986. | MR 838085 | Zbl 0592.60049

[16] S. Goldstein, Antisymmetric functionals of reversible Markov processes, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 31 (1995) 177-190. | Numdam | MR 1340036 | Zbl 0813.60023

[17] G.R. Grimmett, Percolation, Springer, Berlin, 1989. | Zbl 0691.60089

[18] G.R. Grimmett, Percolation and disordered systems, in: P. Bernard (Ed.), Ecole d'Eté de Probabilités de Saint Flour XXVI-1996, Lecture Notes in Mathematics, Vol. 1665, Springer, Berlin, 1997, pp. 153-300. | MR 1490045 | Zbl 0884.60089

[19] G.R. Grimmett and H. Kesten, First-passage percolation, network flows and electrical networks, Z. Wahr. Ver. Geb. 66 (1984) 335-366. | MR 751574 | Zbl 0525.60098

[20] G.R. Grimmett and J.M. Marstrand, The supercritical phase of percolation is well behaved, Proc. Royal Society (London), Ser. A 430 (1990) 439-457. | MR 1068308 | Zbl 0711.60100

[21] G.R. Grimmett, M.V. Menshikov and S.E. Volkov, Random walks in random labyrinths, Markov Process Related Fields 2 (1996) 69-86. | MR 1418408 | Zbl 0879.60108

[22] F. Den Hollander, J. Naudts and F. Redig, Invariance principle for the stochastic Lorentz lattice gas, J. Statist. Phys. 66 (1992) 1583-1598. | MR 1156416 | Zbl 0925.82148

[23] H. Kesten, Percolation Theory for Mathematicians, Birkhäuser, Boston, 1982. | Zbl 0522.60097

[24] C. Kipnis and S.R.S. Varadhan, Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusion, Comm. Math. Phys. 104 (1986) 1-19. | MR 834478 | Zbl 0588.60058

[25] T.M. Liggett, R.H. Schonmann and A. Stacey, Domination by product measures, Ann. Probab. 25 (1997) 71-95. | MR 1428500 | Zbl 0882.60046

[26] H.A. Lorentz, The motion of electrons in metallic bodies, I, II, and III, Koninklijke Akademie van Wetenschappen te Amsterdam, Section of Sciences 7 (1905) 438-453, 585-593, 684-691.

[27] A. Pisztora, Surface order large deviations for Ising, Potts and percolation models, Probab. Theory Related Fields 104 (1996) 427-466. | MR 1384040 | Zbl 0842.60022

[28] A. Quas, Infinite paths in a Lorentz lattice gas model, Probab. Theory Related Fields (1996), to appear. | MR 1701521 | Zbl 0932.60087

[29] B. Tóth, Persistent random walks in random environment, Probab. Theory Related Fields 71 (1986) 615-625. | MR 833271 | Zbl 0589.60099

[30] F. Wang and E.G.D. Cohen, Diffusion in Lorentz lattice gas cellular automata: The honeycomb and quasi-lattices compared with the square and triangular lattices, J. Statist. Phys. 81 (1995) 467-495.

[31] R.M. Ziff, X.P. Kong and E.G.D. Cohen, Lorentz lattice-gas and kinetic-walk model, Phys. Rev. A 44 (1991) 2410-2428.