Local convergence of random graph colorings

Combinatorica, Volume 38, Issue 2, 2017, Pages 341-380.

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Abstract:

Let G = G(n, m) be a random graph whose average degree d = 2m/n is below the k-colorability threshold. If we sample a k-coloring σ of G uniformly at random, what can we say about the correlations between the colors assigned to vertices that are far apart? According to a prediction from statistical physics, for average degrees below the so...More

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