The Mean First Rotation Time of a planar polymer
  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. 
Stavros Vakeroudis (LPMA, ENS, MODAL'X), Marc Yor (LPMA, IUF), David   Holcman (ENS)
math.PR