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Regularity of the SLE(4) uniformizing map and the SLE(8) trace

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We give the modulus of continuity of the SLE (4) uniformizing map. As a consequence of our analysis, we show that the Jones-Smirnov condition for conformal removability does not hold for SLE (4). We also give the modulus of continuity for SLE (8) with the capacity parameterization, proving a conjecture of Alvisio and Lawler.

Based on joint work with Jason Miller and Lukas Schoug.

This talk is part of the Probability series.

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