  Let $\Gamma$ be a graph and $P$ be a reversible random walk on $\Gamma$. From
the $L^2$ analyticity of the Markov operator $P$, we deduce that an iterate of
odd exponent of $P$ is `lazy', that is there exists an integer $k$ such that
the transition probability (for the random walk $P^{2k+1}$) from a vertex $x$
to itself is uniformly bounded from below. The proof does not require the
doubling property on $\Gamma$ but only a polynomial control of the volume.
