The Mean First Rotation Time of a planar polymer

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.

References in corpus (3)

• Narrow escape and leakage of Brownian particles
• Integrability properties and limit theorems for the exit time from a cone of planar Brownian motion
• On hitting times of the winding processes of planar Brownian motion and of Ornstein-Uhlenbeck processes, via Bougerol's identity

Cited by in corpus (2)

• On the optimal designs for the prediction of complex Ornstein-Uhlenbeck processes
• D-optimal designs for complex Ornstein-Uhlenbeck processes