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math.PR2025
Near-critical Ornstein--Zernike theory for the planar random-cluster model
Lucas D'Alimonte, Ioan Manolescu
We develop an Ornstein--Zernike theory for the two-dimensional random-cluster model with that also applies in its near-critical regime. In particular, we prove an asy…
math.PR2025
Exploring the phase transition of planar FK-percolation
Ioan Manolescu
The aim of these notes is to give a quick introduction to FK-percolation, focusing on certain recent results about the phase transition of the two dimensional model, namely its con…