Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-avoiding walks in a rectangle   A celebrated problem in numerical analysis is to consider Brownian motion
originating at the centre of a $10 \times 1$ rectangle, and to evaluate the
ratio of probabilities of a Brownian path hitting the short ends of the
rectangle before hitting one of the long sides. For Brownian motion this
probability can be calculated exactly \cite{BLWW04}. Here we consider instead
the more difficult problem of a self-avoiding walk in the scaling limit, and
pose the same question. Assuming that the scaling limit of SAW is conformally
invariant, we evaluate, asymptotically, the same ratio of probabilities. For
the SAW case we find the probability ratio is approximately 200 times greater
than for Brownian motion.

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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph