Hitting probability for anomalous diffusion processes

Details Hitting probability for anomalous diffusion processes Hitting probability for anomalous diffusion processes

2009-11-19

arxiv.org/abs/0911.3815v1

Phys. Rev. Lett. 104, 020602 (2010)

Physics

Condensed Matter

Statistical Mechanics

5 pages, 4 figures

Scientific paper

10.1103/PhysRevLett.104.020602

We present the universal features of the hitting probability $Q(x,L)$, the probability that a generic stochastic process starting at $x$ and evolving in a box $[0,L]$ hits the upper boundary $L$ before hitting the lower boundary at 0. For a generic self-affine process (describing, for instance, the polymer translocation through a nanopore) we show that $Q(x,L)=Q(x/L)$ and the scaling function $Q(z)\sim z^\phi$ as $z\to 0$ with $\phi=\theta/H$ where $H$ and $\theta$ are respectively the Hurst exponent and the persistence exponent of the process. This result is verified in several exact calculations including when the process represents the position of a particle diffusing in a disordered potential. We also provide numerical supports for our analytical results.

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