Linear speed large deviations for percolation clusters
| dc.creator | Kovchegov, Yevgeniy | |
| dc.creator | Sheffield, Scott | |
| dc.date | 2003-10-16 | |
| dc.date | 2003-12-04 | |
| dc.date.accessioned | 2026-07-07T05:01:59Z | |
| dc.date.available | 2026-07-07T05:01:59Z | |
| dc.description | Let C_n be the origin-containing cluster in subcritical percolation on the lattice (1/n) Z^d, viewed as a random variable in the space Omega of compact, connected, origin-containing subsets of R^d, endowed with the Hausdorff metric delta. When d >= 2, and Gamma is any open subset of Omega, we prove: lim_{n \to \infty}(1/n) \log P(C_n \in Γ) = -\inf_{S \in Γ} λ(S) where lambda(S) is the one-dimensional Hausdorff measure of S defined using the {\em correlation norm}: ||u|| := \lim_{n \to \infty} - \frac{1}{n} \log P (u_n \in C_n) where u_n is u rounded to the nearest element of (1/n)Z^d. Given points a^1, >..., a^k in R^d, there are finitely many correlation-norm Steiner trees spanning these points and the origin. We show that if the C_n are each conditioned to contain the points a^1_n,..., a^k_n, then the probability that C_n fails to approximate one of these trees decays exponentially in n. | |
| dc.description | five pages | |
| dc.identifier | https://arxiv.org/abs/math/0310256 | |
| dc.identifier | http://arxiv.org/abs/math/0310256 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68885 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.title | Linear speed large deviations for percolation clusters | |
| dc.type | text |