Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractal random series generated by Poisson-Voronoi tessellations   In this paper, we construct a new family of random series defined on $\R^D$,
indexed by one scaling parameter and two Hurst-like exponents. The model is
close to Takagi-Knopp functions, save for the fact that the underlying
partitions of $\R^D$ are not the usual dyadic meshes but random Voronoi
tessellations generated by Poisson point processes. This approach leads us to a
continuous function whose random graph is shown to be fractal with explicit and
equal box and Hausdorff dimensions. The proof of this main result is based on
several new distributional properties of the Poisson-Voronoi tessellation on
the one hand, an estimate of the oscillations of the function coupled with an
application of a Frostman-type lemma on the other hand. Finally, we introduce
two related models and provide in particular a box-dimension calculation for a
derived deterministic Takagi-Knopp series with hexagonal bases.

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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat