Factor of iid's through stochastic domination

Ádám Timár

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arXiv · 2306.15120

Factor of iid's through stochastic domination

Ádám Timár

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Abstract

We develop a method to prove that certain percolation processes on amenable random rooted graphs are factors of iid (fiid), given that the process is a monotone limit of random finite subgraphs that satisfy a certain independent stochastic domination property. Among the consequences are the previously open claims that the Uniform Spanning Forest (USF) is a factor of iid for recurrent graphs, it is a finite-valued finitary fiid on amenable graphs, and that the critical Ising model on $\Z^d$ is a finite-valued finitary fiid, using the known uniqueness of the Gibbs measure.

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BibTeX RIS

Ádám Timár. 2023-06-27. Factor of iid's through stochastic domination. https://arxiv.org/abs/2306.15120

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