@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}, pages = {425--487}, publisher = {Gauthier-Villars}, volume = {22}, number = {4}, year = {1986}, mrnumber = {871905}, zbl = {0632.60106}, language = {en}, url = {http://www.numdam.org/item/AIHPB_1986__22_4_425_0/} }
TY - JOUR AU - Kesten, Harry TI - Subdiffusive behavior of random walk on a random cluster JO - Annales de l'I.H.P. Probabilités et statistiques PY - 1986 SP - 425 EP - 487 VL - 22 IS - 4 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPB_1986__22_4_425_0/ LA - en ID - AIHPB_1986__22_4_425_0 ER -
Kesten, Harry. Subdiffusive behavior of random walk on a random cluster. Annales de l'I.H.P. Probabilités et statistiques, Tome 22 (1986) no. 4, pp. 425-487. http://www.numdam.org/item/AIHPB_1986__22_4_425_0/
[1] Density of states on fractals: « fractons » ; J. Physique Lett., t. 43, 1982, L625-631.
and ,[2] Branching Processes, 1972, Springer-Verlag. | MR | Zbl
and ,[3] Probability Theory, 1978, Springer-Verlag. | MR | Zbl
and ,[4] La percolation : un concept unificateur, La Recherche, t. 7, 1976, p. 919-927.
,[5] An invariance principle for reversible Markov processes with application to random motions in random environments, (1985, preprint).
, , and ,[6] Random Walk and Electric Networks, Carus Math. Monograph, No. 22, 1984, Math. Assoc. of America. | MR | Zbl
and ,[7] Conditioned limit theorems for some null recurrent Markov processes, Ann. Probab., t. 6, 1978, p. 798-828. | MR | Zbl
,[8] An Introduction to Probability Theory and its Applications, Vol. I, 3rd ed., John Wiley and Sons, 1968. | MR | Zbl
,[9] Critical phenomena for Spitzer's reversible nearest particle systems, Ann. Probab., t. 10, 1982, p. 881-895. | MR | Zbl
and ,[10] The Theory of Branching Processes, Springer-Verlag and Prentice Hall, 1963. | MR | Zbl
,[11] Probability densities for the displacement of random walks on percolation clusters, J. Phys. A. Math. Gen., t. 18, 1985, L719-722.
, , and ,[12] 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 | Zbl
,[13] Branching Processes with Biological Applications, John Wiley and Sons, 1950. | Zbl
,[14] The critical probability of bond percolation on the square lattice equals 1/2, Comm. Math. Phys., t. 74, 1980, p. 41-59. | MR | Zbl
,[15] Percolation Theory for Mathematicians, Birkhauser-Boston, 1982. | MR | Zbl
,[16] The incipient infinite cluster in two-dimensional percolation, to appear in Theor. Prob. Rel. Fields, 1986. | MR | Zbl
,[17] The diffusion limit for reversible jump processes on Zd with periodic random bond conductivities, Comm. Math. Phys., t. 90, 1983, p. 27-68. | MR | Zbl
,[18] To what class of fractals does the Alexander-Orbach conjecture apply? Phys. Rev. Lett., t. 51, 1983, p. 2048-2051.
and ,[19] Probability Theory, 4th ed., Springer Verlag, 1977. | MR | Zbl
,[20] Solvable fractal family, and its possible relation to the backbone at percolation, Phys. Rev. Lett., t. 47, 1981, p. 1771-1774. | MR
and ,[21] Martingales and Stochastic Integrals I, Lecture Notes in Math, t. 284, 1972, Springer-Verlag. | MR | Zbl
,[22] Diffusion on percolation structures, in Percolation Structures and Processes, Ann. Israel. Phys. Soc., t. 5, 1983, Eds. G. Deutscher, R. Zallen and J. Adler.
and ,[23] Some limit theorems for the total progeny of a branching process, Adv. Appl. Prob., t. 3, 1971, p. 176-192. | MR | Zbl
,[24] Random walk on fractal structures and percolation clusters, J. Physique-Lett., t. 44, 1983, L13-22.
and ,[25] Percolation probabilities on the square lattice, Ann. Discrete Math., t. 3, 1978, p. 227-245. | MR | Zbl
and ,[26] A branching process with mean one and possibly infinite variance, Z. Wahrsch. verw. Geb., t. 9, 1968, p. 139-145. | MR | Zbl
,[27] 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] Inequalities with applications to percolation and reliability, J. Appl. Prob., t. 22, 1985, p. 556-569. | MR | Zbl
and ,