Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Space-time duality for fractional diffusion   Zolotarev proved a duality result that relates stable densities with
different indices. In this paper, we show how Zolotarev duality leads to some
interesting results on fractional diffusion. Fractional diffusion equations
employ fractional derivatives in place of the usual integer order derivatives.
They govern scaling limits of random walk models, with power law jumps leading
to fractional derivatives in space, and power law waiting times between the
jumps leading to fractional derivatives in time. The limit process is a stable
L\'evy motion that models the jumps, subordinated to an inverse stable process
that models the waiting times. Using duality, we relate the density of a
spectrally negative stable process with index $1<\alpha<2$ to the density of
the hitting time of a stable subordinator with index $1/\alpha$, and thereby
unify some recent results in the literature. These results also provide a
concrete interpretation of Zolotarev duality in terms of the fractional
diffusion model.

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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: acc-phys