On the truncated long-range percolation on $\Z^2$

B.N.B. Lima, de, A. Sapozhnikov

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3 Citations (Scopus)

Abstract

We consider an independent long-range bond percolation on Z2. Horizontal and vertical bonds of length n are independently open with probability p_n ¿ [0, 1]. Given ¿n=18¿i=1n(1 - pi) <8, we prove that there exists an infinite cluster of open bonds of length less than or equal to N for some large but finite N. The result gives a partial answer to the truncation problem.
Original languageEnglish
Pages (from-to)287-291
JournalJournal of Applied Probability
Volume45
Issue number1
DOIs
Publication statusPublished - 2008

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