Abstract
We compute the almost-sure Hausdorff dimension of the double points of chordal mathrm {SLE}_kappa for kappa > 4, confirming a prediction of Duplantier–Saleur (1989) for the contours of the FK model. We also compute the dimension of the cut points of chordal mathrm {SLE}_kappa for kappa > 4 as well as analogous dimensions for the radial and whole-plane mathrm {SLE}_kappa (rho ) processes for kappa > 0. We derive these facts as consequences of a more general result in which we compute the dimension of the intersection of two flow lines of the formal vector field e^{ih/chi }, where h is a Gaussian free field and chi > 0, of different angles with each other and with the domain boundary.
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