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Optimal Holder exponent for the SLE path · Around

2009

Optimal Holder exponent for the SLE path

Johansson, Fredrik, Lawler, Gregory F.

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We prove an upper bound on the optimal H\"older exponent for the chordal SLE path parameterized by capacity and thereby establish the optimal exponent as conjectured by J.

Lind.
We also give a new proof of the lower bound.
Our proofs are based on the sharp estimates of moments of the derivative of the inverse map.

Built on

Boundary behaviour of conformal maps
Christian Pommerenke · 1992
Earlier work this paper cites.
Continuous martingales and Brownian motion
Daniel Revuz and Marc Yor · 1999
Earlier work this paper cites.
Scaling limits of loop-erased random walks and uniform spanning trees
Oded Schramm · 2000
Earlier work this paper cites.
Conformal invariance of planar loop-erased random walks and uniform spanning trees
Gregory F. Lawler, Oded Schramm, and Wendelin Werner · 2004
Earlier work this paper cites.

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