  Random walks and diffusions in symmetric random environment are known to
exhibit metastable behavior: they tend to stay for long times in wells of the
environment. For the case that the environment is a one-dimensional two-sided
standard Brownian motion, we study the process of depths of the consecutive
wells of increasing depth that the motion visits. When these depths are looked
in logarithmic scale, they form a stationary renewal cluster process. We give a
description of the structure of this process and derive from it the almost sure
limit behavior and the fluctuations of the empirical density of the process.
