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math.PR2009★ 10 cited
Connection probabilities and RSW-type bounds for the FK Ising model
Hugo Duminil-Copin, Clément Hongler, Pierre Nolin
We prove Russo-Seymour-Welsh-type uniform bounds on crossing probabilities for the FK Ising model at criticality, independent of the boundary conditions. Our proof relies mainly on…
math.PR2009
Critical percolation: the expected number of clusters in a rectangle
Clément Hongler, Stanislav Smirnov
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 se…