Rates of Convergence for the Gibbs Sampler

#### Chuanshu Ji, E. Kira

1997, v.3, Issue 1, 89-102

ABSTRACT

This work concerns the rate of convergence for the Gibbs sampler (Glauber type dynamics) on configuration space $S^{\Lambda}$, where the index set $\Lambda$ is a finite subset of $Z^d$ with cardinality $n$, and the single-spin space $S$ is a finite set with cardinality $s$. Under the Dobrushin-Shlosman condition, an explicit expression of the asymptotic order of convergence is provided in terms of $n$ and $s$ as both $n$ and $s$ tend to infinity.

Keywords: Random fields,Gibbs sampler,rate of convergence,log-Sobolevinequality,spectral gap