The dimension of the SLE curves

Vincent Beffara
2008 Annals of Probability  
Let $\gamma$ be the curve generating a Schramm--Loewner Evolution (SLE) process, with parameter $\kappa\geq0$. We prove that, with probability one, the Hausdorff dimension of $\gamma$ is equal to $\operatorname {Min}(2,1+\kappa/8)$.
doi:10.1214/07-aop364 fatcat:gwirnquh4vfd3m46ial4olxgty