The Mean First Rotation Time of a planar polymer

Stavros Vakeroudis (1, 2, 3) , Marc Yor (1, 4) , David Holcman (2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 ENS-PSL - École normale supérieure - Paris
3 MODAL'X - Modélisation aléatoire de Paris X
4 IUF - Institut universitaire de France

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.

Mots clés: Polymer; Rotation; Stochastic Modeling; Brownian motion

Domaines: Probabilités [math.PR]; Biologie cellulaire

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