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Rapid Mixing for Sampling Colorings of Random Graphs up to Tree Uniqueness Threshold
We study the mixing time of the single-site Glauber dynamics for sampling proper \(q\)-colorings on sparse Erdős-Rényi random graphs \(\mathcal{G}(n, d/n)\). We prove that, whenever \(q \ge (1 + o_d(1))d\), Glauber dynamics mixes in polynomial time with high probability over \(\mathcal{G}(n, d/n)\)
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