The notion of intermittency comes from physics, and involves systems in which most of the energy is concentrated in small regions. For example, most of the energy on the surface of the sun is concentrated in sunspots, and within sunspots there is a similar concentration in yet smaller regions.
The large scale structure of the universe likewise consists of large empty spaces and small regions where matter is concentrated.

The parabolic Anderson model, governed by the following stochastic PDE,

\[\begin{equation*} \partial_tu=\partial_x^2u+u\dot{W} \end{equation*}\]

is a mathematically tractible model exhibiting intermittency which it has been widely studied by probabilists. Here \(x\in\mathbf{R}\) and \(\dot{W}=\dot{W}(t,x)\) is two-parameter white noise.

Solutions to the equation exhibit high peaks separated by large regions where the solution is small. Most papers have dealt with the high peaks.
In work with Davar Khoshnevisan, Kunwoo Kim, and Shang-Yuan Shiu, we develop information about the solution on the regions between the peaks.