Percolation in ∞ + 1 Dimensions
نویسندگان
چکیده
We investigate percolation on the graph of the direct product T × Z of a regular tree T and the line Z, in which each 'tree' edge is open with probability τ and each 'line' edge with probability λ. There are three non-trivial phases, corresponding to the existence of 0, ∞, and 1 infinite open clusters. Such results may be obtained also for the graph T × Z d where d ≥ 2.
منابع مشابه
1 8 M ar 2 00 8 Local Persistence in the Directed Percolation Universality Class
We revisit the problem of local persistence in directed percolation, reporting improved estimates of the persistence exponent in 1+1 dimensions, discovering strong corrections to scaling in higher dimensions, and investigating the mean field limit. Moreover, we examine a graded persistence probability that a site does not flip more than m times and demonstrate how local persistence can be studi...
متن کاملJa n 20 08 Local Persistence in the Directed Percolation Universality Class
We revisit the problem of local persistence in directed percolation, reporting improved estimates of the persistence exponent in 1+1 dimensions, discovering strong corrections to scaling in higher dimensions, and investigating the mean field limit. Moreover, we introduce a graded persistence probability that a site does not flip more than n times and demonstrate how local persistence can be stu...
متن کاملA crossing probability for critical percolation in two dimensions
Langlands et al. considered two crossing probabilities, π h and π hv , in their extensive numerical investigations of critical percolation in two dimensions. Cardy was able to find the exact form of π h by treating it as a correlation function of boundary operators in the Q → 1 limit of the Q state Potts model. We extend his results to find an analogous formula for π hv which compares very well...
متن کاملComment on ‘Topology invariance in percolation thresholds’
In a recent article, Galam and Mauger proposed an invariant for site and bond percolation thresholds, based on known values for twenty lattices (Eur. Phys. J. B 1 (1998) 255–258). Here we give a larger list of values for more than forty lattices in two to six dimensions. The list contains examples of lattices with equal site percolation thresholds, but different bond percolation thresholds. The...
متن کاملThe Time of Bootstrap Percolation in Two Dimensions
We study the distribution of the percolation time T of 2-neighbour bootstrap percolation on [n] with initial set A ∼ Bin([n], p). We determine T up to a constant factor with high probability for all p above the critical probability for percolation, and to within a 1 + o(1) factor for a large range of p.
متن کاملTHE SCALING LAW FOR THE DISCRETE KINETIC GROWTH PERCOLATION MODEL
The Scaling Law for the Discrete Kinetic Growth Percolation Model The critical exponent of the total number of finite clusters α is calculated directly without using scaling hypothesis both below and above the percolation threshold pc based on a kinetic growth percolation model in two and three dimensions. Simultaneously, we can calculate other critical exponents β and γ, and show that the scal...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1990