  In this paper we study the spectral properties of Markov-operator on
$L^{2}$-spaces. Lawler and Sokal (Trans. Amer. Math. Soc., 1988, 309, pp.
557-580) used isoperimetric constants for discrete and continuous time Markov
chains to obtain a spectral gap at 1. For time discrete Markov chains this does
not exclude periodic behavior. We define a new constant measuring the distance
from periodicity and give necessary and sufficient conditions for the existence
of a global spectral gap in terms of this constant.

Probability