Explicit bounds for Dobrushin interdependence coefficients in the log-concave setting

Derive explicit and informative upper bounds for Dobrushin interdependence coefficients associated with log-concave probability measures on R^d, to enable quantitative convergence analysis of Gibbs samplers via Dobrushin’s method.

Background

One classical approach to Gibbs sampler convergence employs Dobrushin interdependence coefficients, which quantify coordinate-wise dependencies and can imply mixing rates under suitable conditions. However, despite the method’s utility, bounding these coefficients can be difficult.

The authors explicitly note that, for log-concave distributions, there are no explicit and informative bounds for these coefficients known, highlighting an open direction for establishing such bounds to complement entropy-based approaches.