  A Markov chain is geometrically ergodic if it converges to its in- variant
distribution at a geometric rate in total variation norm. We study geo- metric
ergodicity of deterministic and random scan versions of the two-variable Gibbs
sampler. We give a sufficient condition which simultaneously guarantees both
versions are geometrically ergodic. We also develop a method for simul-
taneously establishing that both versions are subgeometrically ergodic. These
general results allow us to characterize the convergence rate of two-variable
Gibbs samplers in a particular family of discrete bivariate distributions.
