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

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

We establish an expression of the Loewner energy of a Jordan curve in terms of Werner’s measure on simple loops of SLE 8/3 type. The proof is based on a formula for the change of the Loewner energy under a conformal map that is reminiscent of SLE processes’ conformal restriction …