A new approach to SLE phase transition

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

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