Branched polymers and hyperplane arrangements

We generalize the construction of branched polymers and the notion of the volume of the space of branched polymers studied by Kenyon and Winkler to any central linear hyperplane arrangement A. The volume of the resulting configuration space of branched polymers associated to the central linear hyperplane arrangement A is expressed through the characteristic polynomial of A. We relate the volume of the space of branched polymers to broken circuits and show the cohomology ring of the space of branched polymers to be the Orlik-Solomon algebra.

This is joint work with Alex Postnikov.