Finitely dependent random colorings of bounded degree graphs

Fuente: arXiv

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Detalles Bibliográficos
Autor principal:	Timár, Ádám
Formato:	Preprint
Publicado:	2024
Materias:	Probability
Acceso en línea:	Acceder al recurso
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_version_	1866911784786460672
author	Timár, Ádám
author_facet	Timár, Ádám
contents	We prove that every (possibly infinite) graph of degree at most $d$ has a 4-dependent random proper $4^{d(d+1)/2}$-coloring, and one can construct it as a finitary factor of iid. For unimodular transitive (or unimodular random) graphs we construct an automorphism-invariant (respectively, unimodular) 2-dependent coloring by $3^{d(d+1)/2}$ colors. In particular, there exist random proper colorings for $\Z^d$ and for the regular tree that are 2-dependent and automorphism-invariant, or 4-dependent and finitary factor of iid.
format	Preprint
id	arxiv_https___arxiv_org_abs_2402_17068
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Finitely dependent random colorings of bounded degree graphs Timár, Ádám Probability We prove that every (possibly infinite) graph of degree at most $d$ has a 4-dependent random proper $4^{d(d+1)/2}$-coloring, and one can construct it as a finitary factor of iid. For unimodular transitive (or unimodular random) graphs we construct an automorphism-invariant (respectively, unimodular) 2-dependent coloring by $3^{d(d+1)/2}$ colors. In particular, there exist random proper colorings for $\Z^d$ and for the regular tree that are 2-dependent and automorphism-invariant, or 4-dependent and finitary factor of iid.
title	Finitely dependent random colorings of bounded degree graphs
topic	Probability
url	https://arxiv.org/abs/2402.17068

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