Limit Theorems Of Polynomial Approximation With Exponential Weights
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Limit Theorems of Polynomial Approximation with Exponential Weights
Author: Michael I. Ganzburg
language: en
Publisher: American Mathematical Soc.
Release Date: 2008
The author develops the limit relations between the errors of polynomial approximation in weighted metrics and apply them to various problems in approximation theory such as asymptotically best constants, convergence of polynomials, approximation of individual functions, and multidimensional limit theorems of polynomial approximation.
Limit Theorems of Polynomial Approximation with Exponential Weights
Author: Michael I. Ganzburg
language: en
Publisher: American Mathematical Society(RI)
Release Date: 2014-09-11
The author develops the limit relations between the errors of polynomial approximation in weighted metrics and apply them to various problems in approximation theory such as asymptotically best constants, convergence of polynomials, approximation of individual functions, and multidimensional limit theorems of polynomial approximation.
The Scaling Limit of the Correlation of Holes on the Triangular Lattice with Periodic Boundary Conditions
Author: Mihai Ciucu
language: en
Publisher: American Mathematical Soc.
Release Date: 2009-04-10
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.