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- W2962772081 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 Sigma 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-called condensation threshold d_c, the colors assigned to far away vertices are asymptotically independent [Krzakala et al: PNAS 2007]. We prove this conjecture for k exceeding a certain constant k_0. More generally, we determine the joint distribution of the k-colorings that Sigma induces locally on the bounded-depth neighborhoods of a fixed number of vertices." @default.
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- W2962772081 date "2015-01-01" @default.
- W2962772081 modified "2023-09-26" @default.
- W2962772081 title "Local Convergence of Random Graph Colorings" @default.
- W2962772081 doi "https://doi.org/10.4230/lipics.approx-random.2015.726" @default.
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