Branched Polymers

Details Branched Polymers Branched Polymers

2007-09-14

arxiv.org/abs/0709.2325v1

Mathematics

Probability

20 pages, 11 figures

Scientific paper

Building on and from the work of Brydges and Imbrie, we give an elementary
calculation of the volume of the space of branched polymers of order $n$ 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 of order $n$ has diameter of order $\sqrt{n}$.

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