First passage time processes and subordinated SLE

Details First passage time processes and subordinated SLE First passage time processes and subordinated SLE

2011-02-15

arxiv.org/abs/1102.2966v3

Phys. Rev. E 84, 011134 (2011)

Physics

Condensed Matter

Statistical Mechanics

8 pages, 3 figures

Scientific paper

10.1103/PhysRevE.84.011134

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.

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