Embedding binary sequences into Bernoulli site percolation on Z(3)

作者：Hilario M R; de Lima B N B^*; Nolin P; Sidoravicius V

来源：Stochastic Processes and Their Applications, 2014, 124(12): 4171-4181.

DOI：10.1016/j.spa.2014.07.022

• Percolation of words
• Block renormalization

We investigate the problem of embedding infinite binary sequences into Bernoulli site percolation on Z(d) with parameter p. In 1995, I. Benjamini and H. Kesten proved that, ford 10 and p = 1/2, all sequences can be embedded, almost surely. They conjectured that the same should hold ford 3. We consider d 3 and p E (pc (d), 1 pc (d)), where 13 c(d) %26lt; 1/2 is the critical threshold for site percolation on Zd. We show that there exists an integer M = M (p), such that, a.s., every binary sequence, for which every run of consecutive Os or is contains at least M digits, can be embedded.

• 出版日期2014-12