منابع مشابه
Critical exponents of plane meanders
Meanders form a set of combinatorial problems concerned with the enumeration of self-avoiding loops crossing a line through a given number of points, n. Meanders are considered distinct up to any smooth deformation leaving the line fixed. We use a recently developed algorithm, based on transfer matrix methods, to enumerate plane meanders. This allows us to calculate the number of closed meander...
متن کاملEnumerations of plane meanders
A closed plane meander of order n is a closed self-avoiding loop intersecting an infinite line 2n times. Meanders are considered distinct up to any smooth deformation leaving the line fixed. We have developed an improved algorithm, based on transfer matrix methods, for the enumeration of plane meanders. This allows us to calculate the number of closed meanders up to n = 24. The algorithm is eas...
متن کاملFrom Fully-Packed Loops to Meanders: Exact Exponents
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...
متن کاملA transfer matrix approach to the enumeration of plane meanders
A closed plane meander of order n is a closed self-avoiding curve intersecting an infinite line 2n times. Meanders are considered distinct up to any smooth deformation leaving the line fixed. We have developed an improved algorithm, based on transfer matrix methods, for the enumeration of plane meanders. While the algorithm has exponential complexity, its rate of growth is much smaller than tha...
متن کاملValues of Brownian intersection exponents I: Half-plane exponents
This paper proves conjectures originating in the physics literature regarding the intersection exponents of Brownian motion in a halfplane. For instance, suppose that B and B′ are two independent planar Brownian motions started from distinct points in a half-plane H. Then as t → ∞,
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2000
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/33/21/101