Rapid Mixing from Spectral Independence beyond the Boolean Domain

نویسندگان

چکیده

We extend the notion of spectral independence (introduced by Anari, Liu, and Oveis Gharan [ 4 ]) from Boolean domain to general discrete domains. This property characterises distributions with limited correlations implies that corresponding Glauber dynamics is rapidly mixing. As a concrete application, we show for sampling proper q -colourings mixes in polynomial-time family triangle-free graphs maximum degree Δ provided ≥ ( α * + δ )Δ where ≈ 1.763 unique solution = exp (1/ ) Þ 0 any constant. first efficient algorithm this regime possibly unbounded Δ. Our main tool establishing recursive coupling Goldberg, Martin, Paterson 25 ].

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ژورنال

عنوان ژورنال: ACM Transactions on Algorithms

سال: 2022

ISSN: ['1549-6333', '1549-6325']

DOI: https://doi.org/10.1145/3531008