2014/11/06 by Holroyd, Alexander E.
#05C15 #60C05 #60G10 #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1411.1463
Holroyd and Liggett recently proved the existence of a stationary 1-dependent 4-coloring of the integers, the first stationary k-dependent q-coloring for any k and q. That proof specifies a consistent family of finite-dimensional distributions, but does not yield a probabilistic construction on the whole integer line. Here we prove that the process can be expressed as a finitary factor of an i.i.d. process. The factor is described explicitly, and its coding radius obeys power-law tail bounds.