Hitting probability for anomalous diffusion processes.
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, we show that Q(x,L)=Q(z=x/L) has a scaling Q(z) approximately z;{phi} as z-->0, where phi=theta/H, H, and theta being the Hurst and persistence exponent of the process, respectively. 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 support for our analytical results.
Majumdar
Satya N
SN
CNRS-Université Paris-Sud, LPTMS, UMR8626-Bât. 100, 91405 Orsay Cedex, France.
Rosso
Alberto
A
Zoia
Andrea
A