Jason Cantarella and I just posted our paper "The Symplectic Geometry of Closed Equilateral Random Walkd in 3-Space" to the arXiv.
This paper is in some ways a follow-up to our paper "Probability Theory of Random Polygons from the Quaternionic Viewpoint", which I described before. Again one of the main goals is to find a good way to choose random polygons (see the aforelinked description for why this is interesting), but in the new paper we want to only choose polygons in which all edges are the same length (hence the “equilateral” in the title). This turns out to be much harder…but also rather desirable if you’re interested in polymers since the bonds between monomers in a polymer tend to all be about the same length.
In any case, we’re pretty happy with what we’ve done and we’ve got lots of exciting ideas for our next project.