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arXiv · 1101.1737

The Mean First Rotation Time of a planar polymer

Stavros Vakeroudis·Marc Yor·David Holcman
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Abstract

We estimate the mean first time, called the mean rotation time (MRT), for a planar random polymer to wind around a point. This polymer is modeled as a collection of n rods, each of them being parameterized by a Brownian angle. We are led to study the sum of i.i.d. imaginary exponentials with one dimensional Brownian motions as arguments. We find that the free end of the polymer satisfies a novel stochastic equation with a nonlinear time function. Finally, we obtain an asymptotic formula for the MRT, whose leading order term depends on the square root of n and, interestingly, depends weakly on the mean initial configuration. Our analytical results are confirmed by Brownian simulations.Our analytical results are confirmed by Brownian simulations.

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Stavros Vakeroudis, Marc Yor, David Holcman. 2011-01-10. The Mean First Rotation Time of a planar polymer. https://doi.org/10.1007/s10955-011-0227-6

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