Asymptotic behavior of self-affine processes in semi-infinite domains

Abstract

We propose to model the stochastic dynamics of a polymer passing through a pore (translocation) by means of a fractional Brownian motion, and study its behavior in presence of an absorbing boundary. Based on scaling arguments and numerical simulations, we present a conjecture that provides a link between the persistence exponent $\theta$ and the Hurst exponent $H$ of the process, thus sheding light on the spatial and temporal features of translocation. Furthermore, we show that this conjecture applies more generally to a broad class of self affine processes undergoing anomalous diffusion in bounded domains, and we discuss some significant examples.

4 pages, 3 figures; to be published in Phys. Rev. Lett

References in corpus (2)

• Fractional Laplacian in Bounded Domains
• Probability distributions for polymer translocation

Cited by in corpus (14)

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• Fractional Brownian motion approach to polymer translocation: the governing equation of motion
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• Geometrical optics of large deviations of fractional Brownian motion
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• Path integrals for fractional Brownian motion and fractional Gaussian noise
• First-passage functionals of Brownian motion in logarithmic potentials and heterogeneous diffusion
• Collision number statistics for transport processes
• Probability density of fractional Brownian motion and the fractional Langevin equation with absorbing walls
• First-passage area distribution and optimal fluctuations of fractional Brownian motion
• Critical properties of the Susceptible-Exposed-Infected model with correlated temporal disorder
• Numerical Aspects of Large Deviations
• Functionals of fractional Brownian motion and the three arcsine laws
• Tempered fractional Brownian motion on finite intervals