Anomalous finite-size effects for the mean-squared gyration radius of Gaussian random knots

This is the authors' abstract. We don't add key points for this paper.

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 that the gyration radius R 2 K can be approximated by a power law, R 2 K ~ N 2ν K eff , for several knots, where the effective exponents ν K eff are larger than 0.5 and less than 0.6. Furthermore, 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. Assuming an asymptotic fitting formula, we also discuss possible asymptotic behaviours for R K 2 of Gaussian random polygons.