An analysis of the induced linear operators associated to divide and color models
Preprint, 2019

We study the natural linear operators associated to divide and color (DC) models. The degree of nonuniqueness of the random partition yield- ing 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

Författare

Malin Palo Forsstrom

Jeffrey Steif

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Färgning av slumpmässiga ekvivalensrelationer, slumpvandringar på dynamisk perkolation och bruskänslighet för gränsgrafen i den Erdös-Renyi-slumpgrafsmodellen

Vetenskapsrådet (VR), 2017-01-01 -- 2020-12-31.

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

Knut och Alice Wallenbergs Stiftelse, 2013-01-01 -- 2018-09-01.

Fundament

Grundläggande vetenskaper

Ämneskategorier

Sannolikhetsteori och statistik

Mer information

Senast uppdaterat

2019-11-28