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 $0 <\beta < 1$). |
5. | Publisher | Organizing agency, location | |
6. | Contributor | Sponsor(s) | |
7. | Date | (YYYY-MM-DD) | 1998-07-07 |
8. | Type | Status & genre | Peer-reviewed Article |
8. | Type | Type | |
9. | Format | File format | |
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 |
14. | Coverage | Geo-spatial location, chronological period, research sample (gender, age, etc.) | |
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