For a biased aging continuous-time random walk with finite-mean, infinite-variance waiting times, the long-time position distribution is governed by a fractional advection-diffusion equation in space, while its far tail follows an infinite density that depends on the aging time.
The key idea, based on Eq
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Diffusion equation and rare fluctuations of the biased aging continuous-time random walk model
For a biased aging continuous-time random walk with finite-mean, infinite-variance waiting times, the long-time position distribution is governed by a fractional advection-diffusion equation in space, while its far tail follows an infinite density that depends on the aging time.