Branched Polymers in Two and Three Dimensions

Richard Kenyon
University of British Columbia

A branched polymer is a connected set of unit balls with nonoverlapping interiors. In 2002, Brydges and Imbrie computed the volume of the space of branched polymers with n balls, in 2 and 3 dimensions. We give a combinatorial proof of their results, and use it to get a finer description of the space of polymers. In particular we show that the diameter of a 3D branched polymer on n disks is of order n^(1/2), and give some exact simulations. (This is joint work with Peter Winkler.)

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