Reproduce “Glauber Dynamics for Sampling Colorings: Rapid Mixing above $(1+1/\mathrm{e})Δ$ via Hidden Hard-Core Models” on OpenResearch
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About this paper
Xiongxin Yang
The authors analyze heat-bath Glauber dynamics for uniformly sampling proper graph colorings, where a vertex is recolored with a legal color. Their Bochner-type proof uses hard-core models hidden in color classes to control the chain’s spectral gap. For fixed γ>0 and sufficiently large maximum degree Δ, the gap is at least κγ/n when q≥(1+1/e+γ)Δ; this does not establish γ=0.
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