An Analysis of the Induced Linear Operators Associated to Divide and Color Models

Malin P. Forsström () and Jeffrey E. Steif ()
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Malin P. Forsström: Chalmers University of Technology and Gothenburg University
Jeffrey E. Steif: Chalmers University of Technology and Gothenburg University

Journal of Theoretical Probability, 2021, vol. 34, issue 2, 1043-1060

Abstract: Abstract 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.

Keywords: Divide; and; color; models; 60G99 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-020-01001-4

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