Abstract
AbstractThe concepts of reptation and the tube model have been successfully used to describe the dynamics of a system of entangled polymers. Attempts to apply this model have given rise to questions about the statistics of a polymer, represented by a lattice random walk, and its entanglement with an obstacle net. We have determined the number of ways such a walk can form unentangled closed loops of various types. If one reels in a general random walk from its ends, pulling out unentangled loop, one is left with the so‐called primitive path, which is taken to represent the path of the tube. The probability that an N step random walk has a K step primitive path has been calculated. Asymptotic formulas for this probability are presented.
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