Subdiffusive behavior of random walk on a random cluster
Kesten, Harry
Annales de l'I.H.P. Probabilités et statistiques, Tome 22 (1986), p. 425-487 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPB_1986__22_4_425_0,
     author = {Kesten, Harry},
     title = {Subdiffusive behavior of random walk on a random cluster},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {22},
     year = {1986},
     pages = {425-487},
     mrnumber = {871905},
     zbl = {0632.60106},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_1986__22_4_425_0}
}

Kesten, Harry. Subdiffusive behavior of random walk on a random cluster. Annales de l'I.H.P. Probabilités et statistiques, Tome 22 (1986) pp. 425-487. http://gdmltest.u-ga.fr/item/AIHPB_1986__22_4_425_0/

[1] S. Alexander and R. Orbach, Density of states on fractals: « fractons » ; J. Physique Lett., t. 43, 1982, L625-631.

[2] K.B. Athreya and P.E. Ney, Branching Processes, 1972, Springer-Verlag. | MR 373040 | Zbl 0259.60002

[3] Y.S. Chow and H. Teicher, Probability Theory, 1978, Springer-Verlag. | MR 513230 | Zbl 0399.60001

[4] P.G. De Gennes, La percolation : un concept unificateur, La Recherche, t. 7, 1976, p. 919-927.

[5] A. De Masi, P.A. Ferrari, S. Goldstein and W.D. Wick, An invariance principle for reversible Markov processes with application to random motions in random environments, (1985, preprint).

[6] P.A. Doyle and J.L. Snell, Random Walk and Electric Networks, Carus Math. Monograph, No. 22, 1984, Math. Assoc. of America. | MR 920811 | Zbl 0583.60065

[7] R. Durrett, Conditioned limit theorems for some null recurrent Markov processes, Ann. Probab., t. 6, 1978, p. 798-828. | MR 503953 | Zbl 0398.60023

[8] W. Feller, An Introduction to Probability Theory and its Applications, Vol. I, 3rd ed., John Wiley and Sons, 1968. | MR 228020 | Zbl 0155.23101

[9] D. Griffeath and T.M. Liggett, Critical phenomena for Spitzer's reversible nearest particle systems, Ann. Probab., t. 10, 1982, p. 881-895. | MR 672290 | Zbl 0498.60090

[10] T.E. Harris, The Theory of Branching Processes, Springer-Verlag and Prentice Hall, 1963. | MR 163361 | Zbl 0117.13002

[11] S. Havlin, D. Movshovitz, B. Trus and G.H. Weiss, Probability densities for the displacement of random walks on percolation clusters, J. Phys. A. Math. Gen., t. 18, 1985, L719-722.

[12] C.C. Heyde, On large deviation probabilities in the case of attraction to a non-normal stable law, Sankhya, Ser. A, t. 30, 1968, p. 253-258. | MR 240854 | Zbl 0182.22903

[13] P. Jagers, Branching Processes with Biological Applications, John Wiley and Sons, 1950. | Zbl 0356.60039

[14] H. Kesten, The critical probability of bond percolation on the square lattice equals 1/2, Comm. Math. Phys., t. 74, 1980, p. 41-59. | MR 575895 | Zbl 0441.60010

[15] H. Kesten, Percolation Theory for Mathematicians, Birkhauser-Boston, 1982. | MR 692943 | Zbl 0522.60097

[16] H. Kesten, The incipient infinite cluster in two-dimensional percolation, to appear in Theor. Prob. Rel. Fields, 1986. | MR 859839 | Zbl 0584.60098

[17] R. Künnemann, The diffusion limit for reversible jump processes on Zd with periodic random bond conductivities, Comm. Math. Phys., t. 90, 1983, p. 27-68. | MR 714611 | Zbl 0523.60097

[18] F. Leyvraz and H.E. Stanley, To what class of fractals does the Alexander-Orbach conjecture apply? Phys. Rev. Lett., t. 51, 1983, p. 2048-2051.

[19] M. Loeve, Probability Theory, 4th ed., Springer Verlag, 1977. | MR 651017 | Zbl 0359.60001

[20] B.B. Mandelbrot and S. Kirkpatrick, Solvable fractal family, and its possible relation to the backbone at percolation, Phys. Rev. Lett., t. 47, 1981, p. 1771-1774. | MR 637547

[21] P.A. Meyer, Martingales and Stochastic Integrals I, Lecture Notes in Math, t. 284, 1972, Springer-Verlag. | MR 426145 | Zbl 0239.60001

[22] C.D. Mitescu and J. Roussenq, Diffusion on percolation structures, in Percolation Structures and Processes, Ann. Israel. Phys. Soc., t. 5, 1983, Eds. G. Deutscher, R. Zallen and J. Adler.

[23] A.G. Pakes, Some limit theorems for the total progeny of a branching process, Adv. Appl. Prob., t. 3, 1971, p. 176-192. | MR 283892 | Zbl 0218.60075

[24] R. Rammal and G. Toulouse, Random walk on fractal structures and percolation clusters, J. Physique-Lett., t. 44, 1983, L13-22.

[25] P.D. Seymour and D.J.A. Welsh, Percolation probabilities on the square lattice, Ann. Discrete Math., t. 3, 1978, p. 227-245. | MR 494572 | Zbl 0405.60015

[26] R.S. Slack, A branching process with mean one and possibly infinite variance, Z. Wahrsch. verw. Geb., t. 9, 1968, p. 139-145. | MR 228077 | Zbl 0164.47002

[27] J. Straley, The ant in the labyrinth: diffusion in random networks near the percolation threshold, J. Phys., Solid State Phys., t. C13, 1980, p. 2991-3002.

[28] J. Van Den Berg and H. Kesten, Inequalities with applications to percolation and reliability, J. Appl. Prob., t. 22, 1985, p. 556-569. | MR 799280 | Zbl 0571.60019