  In this note we prove a spectral gap for various Markov chains on various
functional spaces. While proving that a spectral gap exists is relatively
common, explicit estimates seems somewhat rare.These estimates are then used to
apply the concentration inequalities of "Effective limit theorems for Markov
chains with a spectral gap" (most of the present material was part of Section 3
of that article, which has been reduced to its core in the published version).
