Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Anomalous finite-size effects and canonical asymptotic behaviors for the
  mean-squared gyration radius of Gaussian random knots   Anomalously strong finite-size effects have been observed for the mean square
radius of gyration $R^2_K$ of Gaussian random polygons with a fixed knot $K$ as
a function of the number $N$ of polygonal nodes. Through computer simulations
with $N < 2000$, we find for several knots that the gyration radius $R^2_K$ can
be approximated by a power law: $R^2_K \sim N^{2 \nu_{K}^{eff}}$, where the
effective exponents $\nu_{K}^{eff}$ for the knots are larger than 0.5 and less
than 0.6. A crossover occurs for the gyration radius of the trivial knot, when
$N$ is roughly equal to the characteristic length $N_c$ of random knotting. For
the asymptotic behavior of $R^2_K$, however, we find that it is consistent with
the standard one with the scaling exponent 0.5. Thus, although the strong
finite-size effects of $R^2_K$ remain effective for extremely large values of
$N$, they can be matched with the asymptotic behavior of random walks.

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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: math