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In this note, we establish an expression of the Loewner energy of a Jordancurve on the Riemann sphere in terms of Werner's measure on simple loops ofSLE$_{8/3}$ type. The proof is based on a formula for the change of the Loewnerenergy under a conformal map that is reminiscent of the restriction propertiesderived for SLE processes.

A note on Loewner energy, conformal restriction and Werner's measure on self-avoiding loops