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Hausdorff dimension of the SLE curve intersected with the real line · Around

2007

Hausdorff dimension of the SLE curve intersected with the real line

Alberts, Tom, Sheffield, Scott

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We establish an upper bound on the asymptotic probability of an SLE(kappa) curve hitting two small intervals on the real line as the interval width goes to zero, for the range 4 < kappa < 8.

As a consequence we are able to prove that the SLE curve intersected with the real line has Hausdorff dimension 2-8/kappa, almost surely.

Built on

Geometric and fractal properties of Brownian motion and random walk paths in two and three dimensions
Gregory F. Lawler · 1999
Earlier work this paper cites.
SLE and triangles
Julien Dubédat · 2003
Earlier work this paper cites.
Hausdorff dimensions for SLE 6 \rm SLE_{6}
Vincent Beffara · 2004
Earlier work this paper cites.

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