Add to ORKGThe scaling limit of crossing probabilities is believed to satisfy a conformal mapping formula, called Cardy's formula, in two-dimensional percolation at the criticality. The formula has been confirmed to hold for site percolation on the equilateral triangular lattice. In this paper, we show that Cardy's formula could not hold for some two-dimensional triangular and square-type lattices, in particular for some periodic 2D graphs.Comment: 8 pages 2 figure
AbstractIn simulation studies in the physics literature, there is only one pair of graphs which have...
Consider long-range Bernoulli percolation on $\mathbb{Z}^d$ in which we connect each pair of distinc...
AbstractWe study a natural dependent percolation model introduced by Häggström. Consider subcritical...
For the site percolation model on the triangular lattice and certain generalizations for which Cardy...
We consider critical site percolation on the triangular lattice in the upper half-plane. Let u1, u2 ...
We show that crossing probabilities in 2D critical site percolation on the triangular lattice in a p...
It is shown that the critical exponent g1 related to pair-connectiveness and shortest-path (or chemi...
We show that for critical site percolation on the triangular lattice two new observables have confor...
Cardy's formula for the probability pi nu (r) of crossing a rectangular critical percolation system ...
Abstract. We show that crossing probabilities in 2D critical site percolation on the triangular latt...
SLE, Cardy, conformal invariance Let A be an arc on the boundary of the unit disk U. We prove an asy...
International audienceIn recent years, important progress has been made in the field of two-dimensio...
Six percolation models in two dimensions are studied: percolation by sites and by bonds on square, h...
We study critical percolation on a regular planar lattice. Let EG(n) be the expected number of open ...
Abstract. We present three techniques for determining rigorous bounds for site percolation critical ...
AbstractIn simulation studies in the physics literature, there is only one pair of graphs which have...
Consider long-range Bernoulli percolation on $\mathbb{Z}^d$ in which we connect each pair of distinc...
AbstractWe study a natural dependent percolation model introduced by Häggström. Consider subcritical...
For the site percolation model on the triangular lattice and certain generalizations for which Cardy...
We consider critical site percolation on the triangular lattice in the upper half-plane. Let u1, u2 ...
We show that crossing probabilities in 2D critical site percolation on the triangular lattice in a p...
It is shown that the critical exponent g1 related to pair-connectiveness and shortest-path (or chemi...
We show that for critical site percolation on the triangular lattice two new observables have confor...
Cardy's formula for the probability pi nu (r) of crossing a rectangular critical percolation system ...
Abstract. We show that crossing probabilities in 2D critical site percolation on the triangular latt...
SLE, Cardy, conformal invariance Let A be an arc on the boundary of the unit disk U. We prove an asy...
International audienceIn recent years, important progress has been made in the field of two-dimensio...
Six percolation models in two dimensions are studied: percolation by sites and by bonds on square, h...
We study critical percolation on a regular planar lattice. Let EG(n) be the expected number of open ...
Abstract. We present three techniques for determining rigorous bounds for site percolation critical ...
AbstractIn simulation studies in the physics literature, there is only one pair of graphs which have...
Consider long-range Bernoulli percolation on $\mathbb{Z}^d$ in which we connect each pair of distinc...
AbstractWe study a natural dependent percolation model introduced by Häggström. Consider subcritical...