Asymptotic Behavior of Self-Affine Processes in Semi-Infinite Domains

Andrea Zoia, Alberto Rosso, Satya N. Majumdar
2009 Physical Review Letters  
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
more » ... at 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.
doi:10.1103/physrevlett.102.120602 pmid:19392261 fatcat:ncae5a3jkbfblonnzgplsmafoa