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Title:
Self-avoiding walks in a rectangular domain
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Abstract:
A celebrated problem in numerical analysis was posed in {\em The SIAM 100 digit challenge.} It proposed a particle undergoing Brownian motion, starting at the centre of a rectangle of aspect ratio 10:1, and asked for the probability, to ten significant digits, that it hits the end before hitting a side. In fact that problem can be solved exactly, in terms of radicals. Here we discuss the corresponding problem of a self-avoiding walker, in the scaling limit, assumed to be describable by $SLE_{8/3}.$ Our solution provides arbitrary numerical precision.
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