From Fully-Packed Loops to Meanders: Exact Exponents
نویسنده
چکیده
We address the meander problem “enumerate all topologically inequivalent configurations of a closed nonselfintersecting plane curve intersecting a given line through a fixed number of points”. We show that meanders may be viewed as the configurations of a suitable fully-packed loop statistical model defined on a random surface. Using standard results relating critical singularities of a lattice model to its gravitational version on random surfaces, we predict the meander configuration exponent α = (29 + √ 145)/12 and many other meandric exponents.
منابع مشابه
Meanders: Exact Asymptotics
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 t...
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