Expansion for the critical point of site percolation: the first three terms
نویسندگان
چکیده
Abstract We expand the critical point for site percolation on d -dimensional hypercubic lattice in terms of inverse powers 2 , and we obtain first three rigorously. This is achieved using lace expansion.
منابع مشابه
Expansion in n−1 for percolation critical values on the n-cube and Z: the first three terms
Let pc(Qn) and pc(Z) denote the critical values for nearest-neighbour bond percolation on the n-cube Qn = {0, 1}n and on Zn, respectively. Let Ω = n for G = Qn and Ω = 2n for G = Zn denote the degree of G. We use the lace expansion to prove that for both G = Qn and G = Zn, pc(G) = Ω−1 + Ω−2 + 7 2 Ω−3 + O(Ω−4). This extends by two terms the result pc(Qn) = Ω−1 + O(Ω−2) of Borgs, Chayes, van der ...
متن کاملthe effect of using critical discourse analytical tools on the improvement of the learners level of critical thinking in reading comprehension
?it is of utmost priority for an experienced teacher to train the mind of the students, and enable them to think critically and correctly. the most important question here is that how to develop such a crucial ability? this study examines a new way to the development of critical thinking utilizing critical discourse analytical tools. to attain this goal, two classes of senior english la...
study of cohesive devices in the textbook of english for the students of apsychology by rastegarpour
this study investigates the cohesive devices used in the textbook of english for the students of psychology. the research questions and hypotheses in the present study are based on what frequency and distribution of grammatical and lexical cohesive devices are. then, to answer the questions all grammatical and lexical cohesive devices in reading comprehension passages from 6 units of 21units th...
the use of appropriate madm model for ranking the vendors of mci equipments using fuzzy approach
abstract nowadays, the science of decision making has been paid to more attention due to the complexity of the problems of suppliers selection. as known, one of the efficient tools in economic and human resources development is the extension of communication networks in developing countries. so, the proper selection of suppliers of tc equipments is of concern very much. in this study, a ...
15 صفحه اولan 2 00 4 Expansion in n − 1 for percolation critical values on the n - cube and Z n : the first three terms
Let pc(Qn) and pc(Z n) denote the critical values for nearest-neighbour bond percolation on the n-cube Qn = {0, 1} n and on Zn, respectively. Let Ω = n for G = Qn and Ω = 2n for G = Zn denote the degree of G. We use the lace expansion to prove that for both G = Qn and G = Zn, pc(G) = Ω −1 +Ω + 7 2 Ω + O(Ω). This extends by two terms the result pc(Qn) = Ω −1 + O(Ω−2) of Borgs, Chayes, van der Ho...
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: Combinatorics, Probability & Computing
سال: 2021
ISSN: ['0963-5483', '1469-2163']
DOI: https://doi.org/10.1017/s0963548321000365