Fractal Dimension Results for Continuous Time Random Walks.

نویسندگان

  • Mark M Meerschaert
  • Erkan Nane
  • Yimin Xiao
چکیده

Continuous time random walks impose random waiting times between particle jumps. This paper computes the fractal dimensions of their process limits, which represent particle traces in anomalous diffusion.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Random walk through fractal environments.

We analyze random walk through fractal environments, embedded in three-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e., of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, an...

متن کامل

Anomalous diffusion in a quenched-trap model on fractal lattices.

Models with mixed origins of anomalous subdiffusion have been considered important for understanding transport in biological systems. Here one such mixed model, the quenched-trap model (QTM) on fractal lattices, is investigated. It is shown that both ensemble- and time-averaged mean-square displacements (MSDs) show subdiffusion with different scaling exponents, i.e., this system shows weak ergo...

متن کامل

4 A pr 1 99 9 The Upper Critical Dimension of the Abelian Sandpile Model

The existing estimation of the upper critical dimension of the Abelian Sandpile Model is based on a qualitative consideration of avalanches as self-avoiding branching processes. We find an exact representation of an avalanche as a sequence of spanning sub-trees of two-component spanning trees. Using equivalence between chemical paths on the spanning tree and loop-erased random walks, we reduce ...

متن کامل

Fractal Dimension of Graphs of Typical Continuous Functions on Manifolds

If M is a compact Riemannian manifold then we show that for typical continuous function defined on M, the upper box dimension of  graph(f) is as big as possible and the lower box dimension of graph(f) is as small as possible.  

متن کامل

Self-avoiding walks on fractal spaces : exact results and Flory approximation

2014 Self-avoiding walks (SAW) explore the backbone of a fractal lattice, while random walks explore the full lattice. We show the existence of an intrinsic exponent for SAW and examine a simple Flory approximation that uses the spectral dimension of the backbone. Exact results for various fractal lattices show that this approximation is not very satisfactory and that properties of SAW depend o...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Statistics & probability letters

دوره 83 4  شماره 

صفحات  -

تاریخ انتشار 2013