Gibbs Ensembles of Nonintersecting Paths
نویسندگان
چکیده
منابع مشابه
Elliptic enumeration of nonintersecting lattice paths
We enumerate lattice paths in the planar integer lattice consisting of positively directed unit vertical and horizontal steps with respect to a specific elliptic weight function. The elliptic generating function of paths from a given starting point to a given end point evaluates to an elliptic generalization of the binomial coefficient. Convolution gives an identity equivalent to Frenkel and Tu...
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We show that with any finite partially ordered set, P , one can associate a matrix whose determinant factors nicely. As corollaries, we obtain a number of results in the literature about GCD matrices and their relatives. Our main theorem is proved combinatorially using nonintersecting paths in a directed graph.
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We consider an ensemble of N discrete nonintersecting paths starting from equidistant points and ending at consecutive integers. Our first result is an explicit formula for the correlation kernel that allows us to analyze the process as N → ∞. In that limit we obtain a new general class of kernels describing the local correlations close to the equidistant starting points. As the distance betwee...
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Gessel and Viennot have developed a powerful technique for enumerating various classes of plane partitions [GVl, 21. There are two fundamental ideas behind this technique. The first is the observation that most classes of plane partitions that are of interest--either by association with the representation theory of the classical groups, or for purely combinatorial reasons+an be interpreted as c...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2009
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-009-0906-1