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.
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https://hal.archives-ouvertes.fr/hal-00553669
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Submitted on : Monday, May 9, 2011 - 7:22:41 PM
Last modification on : Tuesday, November 19, 2019 - 9:59:27 AM
Long-term archiving on: Wednesday, August 10, 2011 - 2:51:51 AM

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  • HAL Id : hal-00553669, version 3
  • ARXIV : 1101.1737

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Stavros Vakeroudis, Marc Yor, David Holcman. The Mean First Rotation Time of a planar polymer. 2011. ⟨hal-00553669v3⟩

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