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Hausdorff Dimension of the SLE Curve Intersected with the Real Line (2008)

Abstract

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 random set of points in R hit by the curve has Hausdorff dimension 2-8/kappa, almost surely.

Publication details

Download	http://www.math.washington.edu/~ejpecp/viewarticle.php?id=1809
Publisher	Institute of Mathematical Statistics
Contributors	National Science Foundation
Repository	Electronic Journal of Probability (United States)
Keywords	60D05;60K35;28A80; SLE; Hausdorff dimension; Two-point hitting probability
Relation	Figure 1 http://www.math.washington.edu/~ejpecp/include/getdoc.php?id=4460&public=true, Figure 2 http://www.math.washington.edu/~ejpecp/include/getdoc.php?id=4461&public=true, Figure 3 http://www.math.washington.edu/~ejpecp/include/getdoc.php?id=4462&public=true, Figure 4 http://www.math.washington.edu/~ejpecp/include/getdoc.php?id=4463&public=true, Figure 5 http://www.math.washington.edu/~ejpecp/include/getdoc.php?id=4464&public=true, Figure 6 http://www.math.washington.edu/~ejpecp/include/getdoc.php?id=4465&public=true, Figure 7 http://www.math.washington.edu/~ejpecp/include/getdoc.php?id=4466&public=true, Figure 8 http://www.math.washington.edu/~ejpecp/include/getdoc.php?id=4467&public=true, Figure 9 http://www.math.washington.edu/~ejpecp/include/getdoc.php?id=4468&public=true
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