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Preprints, Working Papers, ... Year : 2011

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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Dates and versions

hal-00553669 , version 1 (07-01-2011)
hal-00553669 , version 2 (21-01-2011)
hal-00553669 , version 3 (09-05-2011)

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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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