Unpredictable paths and percolation
نویسندگان
چکیده
منابع مشابه
Unpredictable Paths and Percolation
We construct a nearest-neighbor process {Sn} on Z that is less predictable than simple random walk, in the sense that given the process until time n, the conditional probability that Sn+k = x is uniformly bounded by Ck−α for some α > 1/2. From this process, we obtain a probability measure μ on oriented paths in Z3 such that the number of intersections of two paths chosen independently according...
متن کاملTricolor percolation and random paths in 3D∗
We study “tricolor percolation” on the regular tessellation of R by truncated octahedra, which is the three-dimensional analog of the hexagonal tiling of the plane. We independently assign one of three colors to each cell according to a probability vector p = (p1, p2, p3) and define a “tricolor edge” to be an edge incident to one cell of each color. The tricolor edges form disjoint loops and/or...
متن کاملExtreme paths in oriented two-dimensional percolation
A useful result about leftmost and rightmost paths in two dimensional bond percolation is proved. This result was introduced without proof in [5] in the context of the contact process in continuous time. As discussed here, it also holds for several related models, including the discrete time contact process and two dimensional site percolation. Among the consequences are a natural monotonicity ...
متن کاملDistribution of shortest paths in percolation
We present a scaling Ansatz for the distribution function of the shortest paths connecting any two points on a percolating cluster which accounts for (i) the e ect of the nite size of the system, and (ii) the dependence of this distribution on the site occupancy probability p. We present evidence supporting the scaling Ansatz for the case of two-dimensional percolation. c © 1999 Elsevier Scienc...
متن کاملThe number of open paths in an oriented ̺-percolation model
We study the asymptotic properties of the number of open paths of length n in an oriented ̺-percolation model. We show that this number is enα(̺)(1+o(1)) as n → ∞. The exponent α is deterministic, it can be expressed in terms of the free energy of a polymer model, and it can be explicitely computed in some range of the parameters. Moreover, in a restricted range of the parameters, we even show th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1998
ISSN: 0091-1798
DOI: 10.1214/aop/1022855749