The configuration space of branched polymers

Richard Kenyon, Brown University

This is joint work with Peter Winkler.

In this talk a "branched polymer" will be a connected collection of
unit disks with non-overlapping interiors.

Building on and from the work of Brydges and Imbrie, we give an
elementary calculation of the volume of the space of branched polymers
with n disks in the plane and in 3-space.  Our development reveals
some more general identities, and allows exact random sampling. In
particular we show that a random 3-dimensional branched polymer with
n disks has diameter of order √n.