Meanders: Exact Asymptotics
نویسندگان
چکیده
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 = √ 29( √ 29 + √ 5)/12, and the semi-meander exponent ᾱ = 1+ √ 11( √ 29+ √ 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.
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