Brownian Loop Soup

(http://arxiv.org/abs/math.PR/0304419)
I discovered another interesting-sounding phrase "brownian loop soup". I don't understand it well. What I sortof know is:

1. Some things (certain kinds of fractals) have exact self-similarity, meaning that you can zoom in on a section and have the zoomed-in version look exactly the same as the original image.
2. Some things (other kinds of fractals) have statistical self-similarity, meaning that you can zoom in on a section and have the zoomed-in version look similar to the original image.
3. Sometimes there are numbers (fractal dimensions, for example) that say something about these very corrugated and random objects.
4. Random walks in the plane diffuse outward in a gaussian way. A walk with finite memory also diffuses outward in a gaussian. Self-avoiding walks (they never visit the same place twice - a physical example might be a polymer) require potentially infinite memory, and they're difficult to Monte Carlo simulate (you get stuck). There are easy-to-simulate approximations of self-avoiding walks (loop-erased random walk, "Schramm-Loewner Evolution"?).
5. Random walks and self-avoiding walks display statistical self-similarity.

I presume that "brownian loop soup" is in this tradition - proving probabilistic claims about statistically self-similar paths.