| Summary: | This paper studies the critical and near-critical regimes of the planar random-cluster model on
$\mathbb Z^2$
with cluster-weight
$q\in [1,4]$
using novel coupling techniques. More precisely, we derive the scaling relations between the critical exponents
$\beta $
,
$\gamma $
,
$\delta $
,
$\eta $
,
$\nu $
,
$\zeta $
as well as
$\alpha $
(when
$\alpha \ge 0$
). As a key input, we show the stability of crossing probabilities in the near-critical regime using new interpretations of the notion of the influence of an edge in terms of the rate of mixing. As a byproduct, we derive a generalisation of Kesten’s classical scaling relation for Bernoulli percolation involving the ‘mixing rate’ critical exponent
$\iota $
replacing the four-arm event exponent
$\xi _4$
.
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