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This paper studies the critical and near-critical regimes of the planarrandom-cluster model on $\mathbb Z^2$ with cluster-weight $q\in[1,4]$ usingnovel coupling techniques. More precisely, we derive the scaling relationsbetween the critical exponents $\beta$, $\gamma$, $\delta$, $\eta$, $\nu$,$\zeta$ as well as $\alpha$ (when $\alpha\ge0$). As a key input, we show thestability of crossing probabilities in the near-critical regime using newinterpretations of the notion of influence of an edge in terms of the rate ofmixing. As a byproduct, we derive a generalization of Kesten's classicalscaling relation for Bernoulli percolation involving the ``mixing rate''critical exponent $\iota$ replacing the four-arm event exponent $\xi_4$.

Planar random-cluster model: scaling relations