The Clairvoyant Demon Has a Hard Task
| dc.creator | Gacs, Peter | |
| dc.date | 2003-02-06 | |
| dc.date.accessioned | 2026-07-07T04:54:56Z | |
| dc.date.available | 2026-07-07T04:54:56Z | |
| dc.description | For some m \ge 4, let us color each column of the integer lattice L = Z^2 independently and uniformly into one of m colors. We do the same for the rows, independently from the columns. A point of L will be called blocked if its row and column have the same color. We say that this random configuration percolates if there is a path in L starting at the origin, consisting of rightward and upward unit steps, and avoiding the blocked points. As a problem arising in distributed computing, it has been conjectured that for m \ge 4, the configuration percolates with positive probability. This has now been proved (in a later paper), for large m. Here, we prove that the probability that there is percolation to distance n but not to infinity is not exponentially small in n. This narrows the range of methods available for proving the conjecture. | |
| dc.description | 3 pages | |
| dc.identifier | https://arxiv.org/abs/math/0302059 | |
| dc.identifier | http://arxiv.org/abs/math/0302059 | |
| dc.identifier | Combinatorics, Probability and Computing 9 (2000) 421-424 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66453 | |
| dc.subject | Probability | |
| dc.subject | 82B43; 60K35; 68Q85 | |
| dc.title | The Clairvoyant Demon Has a Hard Task | |
| dc.type | text |