منابع مشابه
Isoradial Bodies
In this paper, we show that for any dimension d ≥ 2 there exists a non-spherical strongly isoradial body i.e., a non-spherical body of constant breadth, such that its orthogonal projections on any subspace has constant inand circumradius. Besides the curiosity aspect of these bodies, they are highly relevant for the analysis of geometric inequalities between the radii and their extreme cases.
متن کاملStatistical mechanics on isoradial graphs
Isoradial graphs are a natural generalization of regular graphs which give, for many models of statistical mechanics, the right framework for studying models at criticality. In this survey paper, we first explain how isoradial graphs naturally arise in two approaches used by physicists: transfer matrices and conformal field theory. This leads us to the fact that isoradial graphs provide a natur...
متن کاملBond Percolation on Isoradial Graphs
In an investigation of percolation on isoradial graphs, we prove the criticality of canonical bond percolation on isoradial embeddings of planar graphs, thus extending celebrated earlier results for homogeneous and inhomogeneous square, triangular, and other lattices. This is achieved via the star–triangle transformation, by transporting the box-crossing property across the family of isoradial ...
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Isoradial dimer models were introduced in Kenyon (Invent Math 150(2):409–439, 2002)— they consist of dimer models whose underlying graph satisfies a simple geometric condition, and whose weight function is chosen accordingly. In this paper, we prove a conjecture of (Kenyon in Invent Math 150(2):409–439, 2002), namely that for periodic isoradial dimer models, the growth rate of the toroidal part...
متن کاملThe Z-invariant massive Laplacian on isoradial graphs
We introduce a one-parameter family of massive Laplacian operators (∆)k∈[0,1) defined on isoradial graphs, involving elliptic functions. We prove an explicit formula for minus the inverse of ∆, the massive Green function, which has the remarkable property of only depending on the local geometry of the graph, and compute its asymptotics. We study the corresponding statistical mechanics model of ...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2004
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-004-1132-4