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[2207.09391] A Near-Linear Time Sampler for the Ising Model
source link: https://arxiv.org/abs/2207.09391
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[Submitted on 19 Jul 2022]
A Near-Linear Time Sampler for the Ising Model
We give a near-linear time sampler for the Gibbs distribution of the ferromagnetic Ising models with edge activities β>1 and external fields λ<1 (or symmetrically, λ>1) on general graphs with bounded or unbounded maximum degree.
Our algorithm is based on the field dynamics given in [CLV21]. We prove the correctness and efficiency of our algorithm by establishing spectral independence of distribution of the random cluster model and the rapid mixing of Glauber dynamics on the random cluster model in a low-temperature regime, which may be of independent interest.
| Subjects: | Probability (math.PR); Data Structures and Algorithms (cs.DS) |
| Cite as: | arXiv:2207.09391 [math.PR] |
| (or arXiv:2207.09391v1 [math.PR] for this version) | |
| https://doi.org/10.48550/arXiv.2207.09391 |
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