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

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• Lévy-walk-like Langevin dynamics
• Arithmetic Brownian motion subordinated by tempered stable and inverse tempered stable processes
• Fractional Brownian motion time-changed by gamma and inverse gamma process
• Subdiffusion in an external force field
• Tempered fractional Langevin-Brownian motion with inverse $\beta$-stable subordinator
• Langevin dynamics for Lévy walk with memory
• Self-similar but not conformally invariant traces obtained by modified Loewner forces
• q-deformed Loewner evolution
• Time-changed Poisson processes of order $k$
• Effect of Random Time Changes on Loewner Hulls