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تسجيل مستخدم جديدA new approach to SLE phase transition
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It is well know that $SLE_kappa$ curves exhibit a phase transition at $kappa=4$. For $kappale 4$ they are simple curves with probability one, for $kappa>4$ they are not. The standard proof is based on the analysis of the Bessel SDE of dimension $d=1+4/kappa$. We propose a different approach which is based on the analysis of the Bessel SDE with $d=1-4/kappa$. This not only gives a new perspective, but also allows to describe the formation of the SLE `bubbles for $kappa>4$.
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