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These sort of questions pop up regularly in the research of a colleague at work. He studies long polymer chains of length $L$ and carbon-carbon length $a$ that are in a liquid.

What is the probability that such a polymer will go round a tube of radius $R$? It is assumed that $a << R < L$.

The problem is not well posed, most probably. What else is necessary to answer? (One could look for a path that is almost closed, within a distance $h$.)

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  • $\begingroup$ Someone here might start by trying to answer a corresponding two dimensional question: a random walk in a plane with a missing disk. $\endgroup$ May 28, 2022 at 21:52
  • $\begingroup$ it seems a lot easier to approach this problem using Montecarlo simulations that by direct analysis $\endgroup$
    – Masacroso
    May 29, 2022 at 6:51
  • $\begingroup$ Both comments are true. Is there any literature on this? $\endgroup$
    – KlausK
    May 29, 2022 at 12:29

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