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The cover of “The Scaling Limit of the Correlation of Holes on the Triangular Lattice with Periodic Boundary Conditions” - Open Library.
The Scaling Limit of the Correlation of Holes on the Triangular Lattice with Periodic Boundary Conditions - cover - The Open Library
Book's cover - The Open Library
The Scaling Limit of the Correlation of Holes on the Triangular Lattice with Periodic Boundary Conditions - cover - Google Books
Book's cover - Google Books

"The Scaling Limit of the Correlation of Holes on the Triangular Lattice with Periodic Boundary Conditions" was published by American Mathematical Society in 2009 - Providence, R.I, the book is classified in Science genre, it has 118 pages and the language of the book is English.


“The Scaling Limit of the Correlation of Holes on the Triangular Lattice with Periodic Boundary Conditions” Metadata:

  • Title: ➤  The Scaling Limit of the Correlation of Holes on the Triangular Lattice with Periodic Boundary Conditions
  • Author:
  • Language: English
  • Number of Pages: 118
  • Is Family Friendly: Yes - No Mature Content
  • Publisher: American Mathematical Society
  • Publish Date:
  • Publish Location: Providence, R.I
  • Genres: Science

“The Scaling Limit of the Correlation of Holes on the Triangular Lattice with Periodic Boundary Conditions” Subjects and Themes:

Edition Specifications:

  • Pagination: p. cm.

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Snippets and Summary:

The author defines the correlation of holes on the triangular lattice under periodic boundary conditions and studies its asymptotics as the distances between the holes grow to infinity.

"The Scaling Limit of the Correlation of Holes on the Triangular Lattice with Periodic Boundary Conditions" Description:

Google Books:

The author defines the correlation of holes on the triangular lattice under periodic boundary conditions and studies its asymptotics as the distances between the holes grow to infinity. He proves that the joint correlation of an arbitrary collection of triangular holes of even side-lengths (in lattice spacing units) satisfies, for large separations between the holes, a Coulomb law and a superposition principle that perfectly parallel the laws of two dimensional electrostatics, with physical charges corresponding to holes, and their magnitude to the difference between the number of right-pointing and left-pointing unit triangles in each hole. The author details this parallel by indicating that, as a consequence of the results, the relative probabilities of finding a fixed collection of holes at given mutual distances (when sampling uniformly at random over all unit rhombus tilings of the complement of the holes) approach, for large separations between the holes, the relative probabilities of finding the corresponding two dimensional physical system of charges at given mutual distances. Physical temperature corresponds to a parameter refining the background triangular lattice. He also gives an equivalent phrasing of the results in terms of covering surfaces of given holonomy. From this perspective, two dimensional electrostatic potential energy arises by averaging over all possible discrete geometries of the covering surfaces.

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  • Public Domain: No
  • Availability Status: Partially available
  • Availability Status for country: US.
  • Available Formats: Text is not avialbe, image copy is available.
  • Google Books Link: Google Books

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