For CLE_κ the mixing rate exponent is 3κ/8 - 1, and this value transfers to FK percolation under the FK-to-CLE scaling limit conjecture.
Conformal loop ensembles: the Markovian characteri- zation and the loop-soup construction
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Mixing rate exponent of planar Fortuin-Kasteleyn percolation
For CLE_κ the mixing rate exponent is 3κ/8 - 1, and this value transfers to FK percolation under the FK-to-CLE scaling limit conjecture.