An Analysis of the Induced Linear Operators Associated to Divide and Color Models
Journal article, 2020

We study the natural linear operators associated to divide and color (DC) models. The degree of nonuniqueness of the random partition yielding a DC model is directly related to the dimension of the kernel of these linear operators. We determine exactly the dimension of these kernels as well as analyze a permutation-invariant version. We also obtain properties of the solution set for certain parameter values which will be important in (1) showing that large threshold discrete Gaussian free fields are DC models and in (2) analyzing when the Ising model with a positive external field is a DC model, both in future work. However, even here, we give an application to the Ising model on a triangle.

Divide and color models


Malin Palö Forsström

Chalmers, Mathematical Sciences, Analysis and Probability Theory

University of Gothenburg

Jeffrey Steif

University of Gothenburg

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Journal of Theoretical Probability

0894-9840 (ISSN) 1572-9230 (eISSN)

Vol. In Press

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Swedish Research Council (VR), 2017-01-01 -- 2020-12-31.

Stochastics for big data and big systems - bridging local and global

Knut and Alice Wallenberg Foundation, 2013-01-01 -- 2018-09-01.

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Control Engineering



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