Related papers: Crossing probability and number of crossing cluste…

The methods of conformal field theory are used to compute the crossing probabilities between segments of the boundary of a compact two-dimensional region at the percolation threshold. These probabilities are shown to be invariant not only…

An exact formula is given for the probability that there exists a spanning cluster between opposite boundaries of an annulus, in the scaling limit of critical percolation. The entire distribution function for the number of distinct spanning…

We present a review of the recent progress on percolation scaling limits in two dimensions. In particular, we will consider the convergence of critical crossing probabilities to Cardy's formula and of the critical exploration path to…

Percolation on a plane is usually associated with clusters spanning two opposite sides of a rectangular system. Here we investigate three-leg clusters generated on a square lattice and spanning the three sides of equilateral triangles. If…

Using methods of conformal field theory, we conjecture an exact form for the probability that n distinct clusters span a large rectangle or open cylinder of aspect ratio k, in the limit when k is large.

Crossing probabilities for critical 2-D percolation on large but finite lattices have been derived via boundary conformal field theory. These predictions agree very well with numerical results. However, their derivation is heuristic and…

These lectures give an introduction to the methods of conformal field theory as applied to deriving certain results in two-dimensional critical percolation: namely the probability that there exists at least one cluster connecting two…

The probability distributions of the masses of the clusters spanning from top to bottom of a percolating lattice at the percolation threshold are obtained in all dimensions from two to five. The first two cumulants and the exponents for the…

Using a recently developed method to simulate percolation on large clusters of distributed machines [N. R. Moloney and G. Pruessner, Phys. Rev. E 67, 037701 (2003)], we have numerically calculated crossing, spanning and wrapping…

The study of crossing probabilities - i.e. probabilities of existence of paths crossing rectangles - has been at the heart of the theory of two-dimensional percolation since its beginning. They may be used to prove a number of results on…

We consider the density of two-dimensional critical percolation clusters, constrained to touch one or both boundaries, in infinite strips, half-infinite strips, and squares, as well as several related quantities for the infinite strip. Our…

We study site percolation on lattices confined to a semi-infinite strip. For triangular and square lattices we find that the probability that a cluster touches the three sides of such a system at the percolation threshold has the continuous…

A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the…

In a recent article, one of the authors used $c=0$ logarithmic conformal field theory to predict crossing-probability formulas for percolation clusters inside a hexagon with free boundary conditions. In this article, we verify these…

Using conformal field theory, we derive several new crossing formulas at the two-dimensional percolation point. High-precision simulation confirms these results. Integrating them gives a unified derivation of Cardy's formula for the…

In this article, we generalize known formulas for crossing probabilities. Prior crossing results date back to J. Cardy's prediction of a formula for the probability that a percolation cluster in two dimensions connects the left and right…

We show that for critical site percolation on the triangular lattice two new observables have conformally invariant scaling limits. In particular the expected number of clusters separating two pairs of points converges to an explicit…

Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount…

Scale-invariant universal crossing probabilities are studied for critical anisotropic systems in two dimensions. For weakly anisotropic standard percolation in a rectangular-shaped system, Cardy's exact formula is generalized using a…

We study a large class of Bernoulli percolation models on random lattices of the half- plane, obtained as local limits of uniform planar triangulations or quadrangulations. We first compute the exact value of the site percolation threshold…