Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entropy and Hausdorff Dimension in Random Growing Trees   We investigate the limiting behavior of random tree growth in preferential
attachment models. The tree stems from a root, and we add vertices to the
system one-by-one at random, according to a rule which depends on the degree
distribution of the already existing tree. The so-called weight function, in
terms of which the rule of attachment is formulated, is such that each vertex
in the tree can have at most K children. We define the concept of a certain
random measure mu on the leaves of the limiting tree, which captures a global
property of the tree growth in a natural way. We prove that the Hausdorff and
the packing dimension of this limiting measure is equal and constant with
probability one. Moreover, the local dimension of mu equals the Hausdorff
dimension at mu-almost every point. We give an explicit formula for the
dimension, given the rule of attachment.

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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: physics