Rapid Mixing from Spectral Independence beyond the Boolean Domain-Reference-Cited by-同舟云学术

Rapid Mixing from Spectral Independence beyond the Boolean Domain

Published:2022-07-31 Issue:3 Volume:18 Page:1-32
ISSN:1549-6325
Container-title:ACM Transactions on Algorithms
language:en
Short-container-title:ACM Trans. Algorithms

Author:

Feng Weiming¹^ORCID,Guo Heng¹^ORCID,Yin Yitong²^ORCID,Zhang Chihao³^ORCID

Affiliation:

1. University of Edinburgh, Edinburgh, UK

2. Nanjing University, Nanjing, Jiangsu, China

3. Shanghai Jiao Tong University, Shanghai, China

Abstract

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

Funder

NSFC

European Research Council

Publisher

Association for Computing Machinery (ACM)

Subject

Mathematics (miscellaneous)

Link

https://dl.acm.org/doi/pdf/10.1145/3531008

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