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