2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167831Let $γ$ be the curve generating a Schramm--Loewner Evolution (SLE) process, with parameter $κ\geq0$. We prove that, with probability one, the Hausdorff dimension of $γ$ is equal to $\operatorname {Min}(2,1+κ/8)$.Published in at http://dx.doi.org/10.1214/07-AOP364 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)ProbabilityComplex Variables60D05, 60G17, 28A80 (Primary)text