  We consider a generalization of the parabolic Anderson model driven by
space-time white noise, also called the stochastic heat equation, on the real
line. High peaks of solutions have been extensively studied under the name of
intermittency, but less is known about spatial regions between peaks, which may
loosely refer to as valleys. We present two results about the valleys of the
solution.
  Our first theorem provides information about the size of valleys and the
supremum of the solution over a valley. More precisely, we show that the
supremum of the solution over a valley vanishes as $t\to\infty$, and we
establish an upper bound of $\exp\{-\text{const}\cdot t^{1/3}\}$ for the rate
of decay. We demonstrate also that the length of a valley grows at least as
$\exp\{+\text{const}\cdot t^{1/3}\}$ as $t\to\infty$.
  Our second theorem asserts that the length of the valleys are eventually
infinite when the initial data has subgaussian tails.
