The diameter of long-range percolation clusters on finite cycles
نویسندگان
چکیده
Bounds for the diameter and expansion of the graphs created by long-range percolation on the cycle Z/NZ, are given.
منابع مشابه
Cycle structure of percolation on high-dimensional tori
In the past years, many properties of the critical behavior of the largest connected components on the high-dimensional torus, such as their sizes and diameter, have been established. The order of magnitude of these quantities equals the one for percolation on the complete graph or Erdős-Rényi random graph, raising the question whether the scaling limits or the largest connected components, as ...
متن کاملJa n 20 09 Bounds for the return probability of the delayed random walk on finite percolation clusters in the critical case
By an eigenvalue comparison-technique[20], the expected return probability of the delayed random walk on critical Bernoulli bond percolation clusters on the twodimensional Euclidean lattice is estimated. The results are generalised to invariant percolations on unimodular graphs with almost surely finite clusters. The approach involves using the special property of cartesian products of finite g...
متن کاملBounds for the return probability of the delayed random walk on finite percolation clusters in the critical case
By an eigenvalue comparison-technique[16], the expected return probability of the delayed random walk on the finite clusters of critical Bernoulli bond percolation on the two-dimensional Euclidean lattice is estimated. The results are generalised to invariant percolations on unimodular graphs with almost surely finite clusters. A similar method has been used elsewhere[17] to derive bounds for i...
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 کاملHeat Kernel Upper Bounds on Long Range Percolation Clusters
In this paper, we derive upper bounds for the heat kernel of the simple random walk on the infinite cluster of a supercritical long range percolation process. For any d ≥ 1 and for any exponent s ∈ (d, (d + 2) ∧ 2d) giving the rate of decay of the percolation process, we show that the return probability decays like t− /s−d up to logarithmic corrections, where t denotes the time the walk is run....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Random Struct. Algorithms
دوره 19 شماره
صفحات -
تاریخ انتشار 2001