Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 203 / 3 / b

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- Solution b

Solution

The Conformal Markov property of SLE says that, conditionally on

(K_{s})_{s \leq t}

, the future hulls

K_{s} = (g_{t} - U_{t}) (K_{t + s} ∖ K_{t})

have the law of a fresh SLE in

(H, 0, \infty)

and are independent of the past, with the usual interpretation of mapping out the old hull.

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