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Almost All Words Are Seen In Critical Site Percolation On The Triangular Lattice


 
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1. Title Title of document Almost All Words Are Seen In Critical Site Percolation On The Triangular Lattice
 
2. Creator Author's name, affiliation, country Harry Kesten; Cornell University
 
2. Creator Author's name, affiliation, country Vladas Sidoravicius; IMPA
 
2. Creator Author's name, affiliation, country Yu Zhang; University of Colorado
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) Percolation, Triangular lattice
 
3. Subject Subject classification Primary 60K35
 
4. Description Abstract We consider critical site percolation on the triangular lattice, that is, we choose $X(v) = 0$ or 1 with probability 1/2 each, independently for all vertices $v$ of the triangular lattice. We say that a word $(\xi_1, \xi_2,\dots) \in \{0,1\}^{\Bbb N}$ is seen in the percolation configuration if there exists a selfavoiding path $(v_1, v_2, \dots)$ on the triangular lattice with $X(v_i) = \xi_i, i \ge 1$. We prove that with probability 1 "almost all" words, as well as all periodic words, except the two words $(1,1,1, \dots)$ and $(0,0,0,\dots)$, are seen. "Almost all" words here means almost all with respect to the measure $\mu_\beta$ under which the $\xi_i$ are i.i.d. with $\mu_\beta {\xi_i = 0}=1 - \mu_\beta {\xi_i = 1} = \beta$ (for an arbitrary $0 <\beta < 1$).
 
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7. Date (YYYY-MM-DD) 1998-07-07
 
8. Type Status & genre Peer-reviewed Article
 
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9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/32
 
10. Identifier Digital Object Identifier 10.1214/EJP.v3-32
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 3
 
12. Language English=en en
 
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