Crossing Probabilities in Topological Rectangles for the Critical Planar FK-Ising model

We consider the FK-Ising model in two dimensions at criticality. We obtain bounds on crossing probabilities of arbitrary topological rectangles, uniform with respect to the boundary conditions, generalizing results of [DCHN11] and [CS12]. Our result relies on new discrete complex analysis techniques, introduced in [Che12]. We detail some applications, in particular the computation of so-called universal exponents, the proof of quasi-multiplicativity properties of arm probabilities, and bounds on crossing probabilities for the classical Ising model


Published in:
Electronic Journal of Probability, 21, 1, 1-28
Year:
2016
Publisher:
Seattle, Institute of Mathematical Statistics
ISSN:
1083-6489
Keywords:
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 Record created 2014-07-21, last modified 2018-03-17

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