The Convergence rate of the Gibbs sampler for the $2-$D Ising model via a geometric bound

Brice Franke; Amine Helali

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arXiv · 1804.09198

The Convergence rate of the Gibbs sampler for the $2-$D Ising model via a geometric bound

Brice Franke·Amine Helali

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Abstract

We study the geometric bound introduced by Diaconis and Stroock $(1991)$ of the Gibbs sampler for the two-dimensional Ising model with free boundary condition. The obtained result generalizes the method proposed by Shiu and Chen $(2015)$ from dimension one to dimension two. Furthermore we observe that the new bound improves the result given by Ingrassia $(1994)$.

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Brice Franke, Amine Helali. 2018-04-24. The Convergence rate of the Gibbs sampler for the $2-$D Ising model via a geometric bound. https://arxiv.org/abs/1804.09198

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