  It is well known that for a strictly stationary, reversible, Harris recurrent
Markov chain, the $\rho$-mixing condition is equivalent to geometric ergodicity
and to a "spectral gap" condition. In this note, it will be shown with an
example that for that class of Markov chains, the "interlaced" variant of the
$\rho$-mixing condition fails to be equivalent to those conditions.
