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arXiv · 0811.1951

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

Andrea Zoia·Alberto Rosso·Satya N. Majumdar
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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 $θ$ 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.

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Andrea Zoia, Alberto Rosso, Satya N. Majumdar. 2009-03-08. Asymptotic behavior of self-affine processes in semi-infinite domains. https://doi.org/10.1103/physrevlett.102.120602

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