2007/09/14 by Richard Kenyon, RICHARD L. KENYON, Peter Winkler +2
Chemistry · Materials Science · Mathematics · Physics and Astronomy · #82B21 #82D60 #Advanced Polymer Synthesis and Characterization #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Polymer crystallization and properties #Probability (math.PR) #math-ph #math.MP #math.PR #msc:82B21 #msc:82D60
paper · pdf · doi:10.48550/arxiv.0709.2325
20 pages, 11 figures
arxiv created 2007/09/14 · openalex publication_date 2007/09/14 · arxiv updated 2009/12/01 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
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 √(n).