  We consider gapped systems governed by either quantum or Markov dynamics,
with the low-lying states below the gap being approximately degenerate. For a
broad class of dynamics, we prove that ground or stationary state correlation
functions can be written as a piece decaying exponentially in space plus a term
set by matrix elements between the low-lying states. The key to the proof is a
local approximation to the negative energy, or annihilation, part of an
operator in a gapped system. Applications to numerical simulation of quantum
systems and to networks are discussed.
