%0 Journal Article %1 kesten1986subdiffusive %A Kesten, Harry %D 1986 %J Ann. Inst. H. Poincaré Probab. Statist. %K fractal_landscape percolation percolation_clusters random_walk %N 4 %P 425--487 %T Subdiffusive behavior of random walk on a random cluster %U http://www.numdam.org/item?id=AIHPB_1986__22_4_425_0 %V 22 %X The author considers the limiting behavior of simple random walks Xn on two types of random graphs: the family tree of a critical branching process, and the incipient infinite cluster of the critical two-dimensional bond percolation model. In each case, he shows that the limiting behavior is subdiffusive in the sense that Xn behaves like nα for some power α<12. The results are most complete in the branching model, for which the result is that, when normalized by n1/3, the distance from Xn to the root of the family tree has a limiting distribution. The proofs are quite long and complex.

@article{kesten1986subdiffusive, abstract = {The author considers the limiting behavior of simple random walks Xn on two types of random graphs: the family tree of a critical branching process, and the incipient infinite cluster of the critical two-dimensional bond percolation model. In each case, he shows that the limiting behavior is subdiffusive in the sense that Xn behaves like nα for some power α<12. The results are most complete in the branching model, for which the result is that, when normalized by n1/3, the distance from Xn to the root of the family tree has a limiting distribution. The proofs are quite long and complex. }, added-at = {2013-09-04T23:17:43.000+0200}, author = {Kesten, Harry}, biburl = {https://www.bibsonomy.org/bibtex/2a0fb8abfd28bbc0789020ad2e6978c55/peter.ralph}, coden = {AHPBAR}, fjournal = {Annales de l'Institut Henri Poincar\'e. Probabilit\'es et Statistique}, interhash = {920f483196659ba8b91d5f5d3edac5b2}, intrahash = {a0fb8abfd28bbc0789020ad2e6978c55}, issn = {0246-0203}, journal = {Ann. Inst. H. Poincar\'e Probab. Statist.}, keywords = {fractal_landscape percolation percolation_clusters random_walk}, mrclass = {60K35 (60J15)}, mrnumber = {871905 (88b:60232)}, mrreviewer = {T. M. Liggett}, number = 4, pages = {425--487}, timestamp = {2013-09-04T23:17:43.000+0200}, title = {Subdiffusive behavior of random walk on a random cluster}, url = {http://www.numdam.org/item?id=AIHPB_1986__22_4_425_0}, volume = 22, year = 1986 }