no. 4
A note on Loewner energy, conformal restriction and Werner’s measure on self-avoiding loops
[Note sur l’énergie de Loewner, la restriction conforme et la mesure de Werner sur les boucles auto-évitantes]
Wang, Yilin1
1 Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Avenue, Cambridge MA (USA)
Annales de l'Institut Fourier, Tome 71 (2021) no. 4, pp. 1791-1805.

Nous établissons une expression de l’énergie de Loewner d’une courbe de Jordan en termes de la mesure de Werner sur les boucles auto-évitantes du type SLE8/3. La preuve est basée sur la variation de l’énergie de Loewner sous l’effet des transformations conformes. Cette formule rappelle la propriété de la restriction conforme de SLE.

We establish an expression of the Loewner energy of a Jordan curve in terms of Werner’s measure on simple loops of SLE8/3 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 property.

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DOI : 10.5802/aif.3427
Classification : 30C55, 60J67
Keywords: Loewner energy, conformal restriction, Werner’s measure, Schramm–Loewner evolution
Mots-clés : énergie de Loewner, restriction conforme, mesure de Werner, evolution Schramm–Loewner

Wang, Yilin 1

1 Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Avenue, Cambridge MA (USA)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {A note on {Loewner} energy, conformal restriction and {Werner{\textquoteright}s} measure on self-avoiding loops},
     journal = {Annales de l'Institut Fourier},
     pages = {1791--1805},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {71},
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Wang, Yilin. A note on Loewner energy, conformal restriction and Werner’s measure on self-avoiding loops. Annales de l'Institut Fourier, Tome 71 (2021) no. 4, pp. 1791-1805. doi : 10.5802/aif.3427. https://aif.centre-mersenne.org/articles/10.5802/aif.3427/

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