Exceptional Planes of Percolation
نویسندگان
چکیده
Consider the standard continuous percolation in R 4 , and choose the parameters so that the induced percolation on a xed two dimensional linear subspace is critical. Although two dimensional critical percolation dies, we show that there are exceptional two dimensional linear subspaces, in which percolation occurs.
منابع مشابه
Local time on the exceptional set of dynamical percolation, and the Incipient Infinite Cluster
In dynamical critical site percolation on the triangular lattice or bond percolation on Z , we define and study a local time measure on the exceptional times at which the origin is in an infinite cluster. We show that at a typical time with respect to this measure, the percolation configuration has the law of Kesten’s Incipient Infinite Cluster. In the most technical result of this paper, we sh...
متن کاملQuantitative noise sensitivity and exceptional times for percolation
One goal of this paper is to prove that dynamical critical site percolation on the planar triangular lattice has exceptional times at which percolation occurs. In doing so, new quantitative noise sensitivity results for percolation are obtained. The latter is based on a novel method for controlling the “level k” Fourier coefficients via the construction of a randomized algorithm which looks at ...
متن کاملLine Percolation in Finite Projective Planes
We study combinatorial parameters of a recently introduced bootstrap percolation problem in finite projective planes. We present sharp results on the size of the minimum percolating sets and the maximal non-percolating sets. Additional results on the minimal and maximal percolation time as well as on the critical probability in the projective plane are also presented.
متن کاملGeometry of curves with exceptional secant planes
We study curves with linear series that are exceptional with regard to their secant planes. Working in the framework of an extension of Brill-Noether theory to pairs of linear series, we prove that a general curve of genus g has no exceptional secant planes, in a very precise sense. We also address the problem of computing the number of linear series with exceptional secant planes in a one-para...
متن کاملThe Fourier Spectrum of Critical Percolation
Consider the indicator function f of a two-dimensional percolation crossing event. In this paper, the Fourier transform of f is studied and sharp bounds are obtained for its lower tail in several situations. Various applications of these bounds are derived. In particular, we show that the set of exceptional times of dynamical critical site percolation on the triangular grid in which the origin ...
متن کامل