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

TL;DR

This paper models polymer translocation as fractional Brownian motion with an absorbing boundary, proposing a conjecture linking persistence and Hurst exponents, applicable to various self-affine processes in bounded domains.

Contribution

It introduces a conjecture connecting the persistence exponent and Hurst exponent for self-affine processes in bounded domains, supported by scaling arguments and numerical simulations.

Findings

Proposes a conjecture linking persistence and Hurst exponents.

Demonstrates applicability to a broad class of self-affine processes.

Provides numerical evidence supporting the conjecture.

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.