Sampling Colorings and Independent Sets of Random Regular Bipartite Graphs in the Non-Uniqueness Region

  title={Sampling Colorings and Independent Sets of Random Regular Bipartite Graphs in the Non-Uniqueness Region},
  author={Zongchen Chen and Andreas Galanis and Daniel Stefankovic and Eric Vigoda},
For spin systems, such as the $q$-colorings and independent-set models, approximating the partition function in the so-called non-uniqueness region, where the model exhibits long-range correlations, is typically computationally hard for bounded-degree graphs. We present new algorithmic results for approximating the partition function and sampling from the Gibbs distribution for spin systems in the non-uniqueness region on random regular bipartite graphs. We give an $\mathsf{FPRAS}$ for counting… 
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