Duality of Schramm-Loewner evolutions

Dubédat, Julien

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 42 (2009) no. 5, pp. 697-724.

On démontre dans cette note une version de la dualité conjecturée pour les évolutions de Schramm-Loewner, en établissant des identités en distribution exactes entre certains arcs de ${\mathrm{SLE}}_{\kappa }$ chordal, $\kappa >4$, et des versions appropriées de ${\mathrm{SLE}}_{\widehat{\kappa }}$, $\widehat{\kappa }=16/\kappa$.

In this note, we prove a version of the conjectured duality for Schramm-Loewner Evolutions, by establishing exact identities in distribution between some boundary arcs of chordal ${\mathrm{SLE}}_{\kappa }$, $\kappa >4$, and appropriate versions of ${\mathrm{SLE}}_{\widehat{\kappa }}$, $\widehat{\kappa }=16/\kappa$.

Classification : 60G17, 60K35
Keywords: Schramm-Loewner evolution, duality, partition function
Mot clés : Évolution de Schramm-Loewner, dualité, fonction de partition

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