First passage time processes and subordinated SLE

Abstract

We study the first passage time processes of anomalous diffusion on self similar curves in two dimensions. The scaling properties of the mean square displacement and mean first passage time of the ballistic motion, fractional Brownian motion and subordinated walk on different fractal curves (loop erased random walk, harmonic explorer and percolation front) are derived. We also define natural parametrized subordinated Schramm Loewner evolution (NS-SLE) as a mathematical tool that can model diffusion on fractal curves. The scaling properties of the mean square displacement and mean first passage time for NS-SLE are obtained by numerical means.

8 pages, 3 figures

References in corpus (7)

• 2D growth processes: SLE and Loewner chains
• A Guide to Stochastic Loewner Evolution and its Applications
• Leapover lengths and first passage time statistics for Lévy flights
• Global properties of Stochastic Loewner evolution driven by Levy processes
• Exact sampling of self-avoiding paths via discrete Schramm-Loewner evolution
• First passage times and distances along critical curves
• Outflow probability for drift--diffusion dynamics