The authors of this paper repeatedly use the term "algebraic tail" when describing some of the distributions they observed:

...the probability of remaining in a small, spatially confined region for a time T is dominated by algebraically long tails that attenuate the superdiffusive spread...


Despite systematic deviations for short distances, all distributions show an algebraic tail with the same exponent $\beta \approx 0.6$, which confirms that the observed power-law is an intrinsic and universal property of dispersal.


Therefore, we conclude that the slow decay in $P_0(t)$ reflects the effect of an algebraic tail in the distribution of rests $\phi(t)$ between displacements.

I haven't been able to find a definition of this term anywhere else. Are they just using it as a synonym for "tail of a power law distribution", or are they referring to a particular subtype of power-law distribution, or something else entirely?


D. Brockmann et al., The scaling laws of human travel, Nature 439, 462 (2005).


1 Answer 1


Yes, this appears to be a synonym with a power-law tail behavior (i.e., decays slower than exponential). Here are some other references to this behavior:

http://www.math.columbia.edu/~chekhlov/PhysRevLetters.77.15.1996.pdf http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3136455/


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