Add to ORKGIt is well-known in percolation theory (and intuitively plausible) that two events of the form ``there is an open path from $s$ to $a$' are positively correlated. We prove the (not intuitively obvious) fact that this is still true if we condition on an event of the form ``there is no open path from $s$ to $t$'
AbstractIn simulation studies in the physics literature, there is only one pair of graphs which have...
We establish the sharpness of the phase transition for a wide class of Gaussian percolation models, ...
We prove a conjecture of Joag-Dev and Goel that if M = M(σ) = {i: σ(i) = i} is the (random) match se...
It is well-known in percolation theory (and intuitively plausible) that two events of the form ``the...
Consider ordinary bond percolation on a finite or countably infinite graph. Let s, t, a and b be ver...
AbstractLet v(A) be the extinction probability for a contact process on a countable set S with initi...
International audienceA useful result about leftmost and rightmost paths in two dimensional bond per...
We study the effect of positive correlations on the critical threshold of site and bond percolation ...
AbstractAn inequality is given that enables one to estimate the probability of a conjunction by the ...
Abstract. Consider a randomly oriented graph G = (V, E) and let a, s and b be three distinct vertice...
AbstractA well-known inequality due to Harris and Kleitman [T.E. Harris, A lower bound for the criti...
Recently van den Berg and Kesten have obtained a correlation-like inequality for Bernoulli sequences...
Percolation is the paradigm for random connectivity and has been one of the most applied statistical...
. We discuss inequalities and applications for percolation and randomcluster models. The relevant ar...
A general method is given whereby m-connectedness correlation functions can be studied in the percol...
AbstractIn simulation studies in the physics literature, there is only one pair of graphs which have...
We establish the sharpness of the phase transition for a wide class of Gaussian percolation models, ...
We prove a conjecture of Joag-Dev and Goel that if M = M(σ) = {i: σ(i) = i} is the (random) match se...
It is well-known in percolation theory (and intuitively plausible) that two events of the form ``the...
Consider ordinary bond percolation on a finite or countably infinite graph. Let s, t, a and b be ver...
AbstractLet v(A) be the extinction probability for a contact process on a countable set S with initi...
International audienceA useful result about leftmost and rightmost paths in two dimensional bond per...
We study the effect of positive correlations on the critical threshold of site and bond percolation ...
AbstractAn inequality is given that enables one to estimate the probability of a conjunction by the ...
Abstract. Consider a randomly oriented graph G = (V, E) and let a, s and b be three distinct vertice...
AbstractA well-known inequality due to Harris and Kleitman [T.E. Harris, A lower bound for the criti...
Recently van den Berg and Kesten have obtained a correlation-like inequality for Bernoulli sequences...
Percolation is the paradigm for random connectivity and has been one of the most applied statistical...
. We discuss inequalities and applications for percolation and randomcluster models. The relevant ar...
A general method is given whereby m-connectedness correlation functions can be studied in the percol...
AbstractIn simulation studies in the physics literature, there is only one pair of graphs which have...
We establish the sharpness of the phase transition for a wide class of Gaussian percolation models, ...
We prove a conjecture of Joag-Dev and Goel that if M = M(σ) = {i: σ(i) = i} is the (random) match se...