Point Transformations and the Relationships Among Anomalous Diffusion, Normal Diffusion and the Central Limit Theorem

@article{Kouri2017PointTA,
  title={Point Transformations and the Relationships Among Anomalous Diffusion, Normal Diffusion and the Central Limit Theorem},
  author={Donald Kouri and Nikhil N. Pandya and Cameron L. Williams and Bernhard G. Bodmann and Jie Yao},
  journal={arXiv: Mathematical Physics},
  year={2017},
  pages={178-197}
}
We present new connections among anomalous diffusion (AD), normal diffusion (ND) and the Central Limit Theorem. This is done by defining a point transformation to a new position variable, which we postulate to be Cartesian, motivated by considerations from super-symmetric quantum mechanics. Canonically quantizing in the new position and momentum variables according to Dirac gives rise to generalized negative semi-definite and self-adjoint Laplacian operators. These lead to new generalized… 

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