Meanders: Exact Asymptotics
arXiv:cond-mat/9910453 · doi:10.1016/S0550-3213(99)00753-1
Abstract
We conjecture that meanders are governed by the gravitational version of a c=-4 two-dimensional conformal field theory, allowing for exact predictions for the meander configuration exponent α=\sqrt{29}(\sqrt{29}+\sqrt{5})/12, and the semi-meander exponent {\barα}=1+\sqrt{11}(\sqrt{29}+\sqrt{5})/24. This result follows from an interpretation of meanders as pairs of fully packed loops on a random surface, described by two c=-2 free fields. The above values agree with recent numerical estimates. We generalize these results to a score of meandric numbers with various geometries and arbitrary loop fugacities.
new version with note added in proof
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